See Witt group in All languages combined, or Wiktionary
{
"etymology_text": "Named after German mathematician Ernst Witt (1911–1991), who introduced the concept in 1937.",
"forms": [
{
"form": "Witt groups",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Witt group (plural Witt groups)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"_dis1": "32 36 32",
"word": "Witt decomposition"
},
{
"_dis1": "32 36 32",
"word": "Witt index"
},
{
"_dis1": "32 36 32",
"word": "Witt ring"
},
{
"_dis1": "32 36 32",
"word": "Witt vector"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebraic geometry",
"orig": "en:Algebraic geometry",
"parents": [
"Algebra",
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Category theory",
"orig": "en:Category theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "31 33 35",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "22 40 38",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 35 32",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 36 31",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "27 38 34",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "27 38 34",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "1995, Raman Parimala, “Study of quadratic forms - Some connections with geometry”, in S. D. Chatterji, editor, Proceedings of the International Congress of Mathematicians, Zürich m94, Birkhäuser, page 328:",
"text": "A general method of studying the Witt group of a smooth variety is through the graded group associated to the filtration induced by the filtration of the Witt group of the function field by powers of the fundamental ideal of even rank forms.",
"type": "quote"
},
{
"text": "2011, Marco Schlichting, Higher Algebraic K-theory, Guillermo Cortiñas (editor), Topics in Algebraic and Topological K-Theory, Springer, Lecture Notes in Mathematics 2008, page 167,\nThe second reason for this emphasis is that an analog of the Thomason-Waldhausen Localization Theorem also holds for many other (co-) homology theories besides K-theory, among which Hochschild homology, (negative, periodic, ordinary) cyclic homology [49], topological Hochschild (and cyclic) homology [2], triangular Witt groups [6] and higher Grothendieck–Witt groups [77]."
},
{
"ref": "2020, Matthias Wendt, “Oriented Schubert calculus in Chow-Witt rings of Grassmannians”, in Federico Binda, Marc Levine, Manh Toan Nguyen, Oliver Röndigs, editors, Motivic Homotopy Theory and Refined Enumerative Geometry, American Mathematical Society, pages 239–240:",
"text": "The Witt group of a category with duality is given as the quotient of the isometry classes of symmetric spaces modulo metabolic spaces.[…]For coherent and derived Witt groups, the derived tensor product of complexes gives rise to duality-preserving functions and consequently to pairings in triangular Witt groups, cf. [GN03].",
"type": "quote"
}
],
"glosses": [
"Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"id": "en-Witt_group-en-noun-fQxBuJVE",
"links": [
[
"algebra",
"algebra"
],
[
"field",
"field"
],
[
"characteristic",
"characteristic"
],
[
"abelian group",
"abelian group"
],
[
"equivalence class",
"equivalence class"
],
[
"nondegenerate",
"nondegenerate"
],
[
"symmetric",
"symmetric"
],
[
"bilinear form",
"bilinear form"
],
[
"equivalence relation",
"equivalence relation"
],
[
"metabolic quadratic space",
"metabolic quadratic space"
],
[
"group operation",
"group operation"
],
[
"orthogonal",
"orthogonal"
],
[
"direct sum",
"direct sum"
],
[
"algebraic geometry",
"algebraic geometry"
],
[
"variety",
"variety"
],
[
"quotient",
"quotient"
],
[
"Grothendieck group",
"Grothendieck group"
],
[
"isometry",
"isometry"
],
[
"class",
"class"
],
[
"modulo",
"modulo"
],
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"duality",
"duality"
]
],
"raw_glosses": [
"(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebraic geometry",
"orig": "en:Algebraic geometry",
"parents": [
"Algebra",
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Category theory",
"orig": "en:Category theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "31 33 35",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "22 40 38",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 35 32",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 36 31",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "27 38 34",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "27 38 34",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;\n(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces\n(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.",
"given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces"
],
"id": "en-Witt_group-en-noun-o0t0obqC",
"links": [
[
"algebra",
"algebra"
],
[
"field",
"field"
],
[
"characteristic",
"characteristic"
],
[
"abelian group",
"abelian group"
],
[
"equivalence class",
"equivalence class"
],
[
"nondegenerate",
"nondegenerate"
],
[
"symmetric",
"symmetric"
],
[
"bilinear form",
"bilinear form"
],
[
"equivalence relation",
"equivalence relation"
],
[
"metabolic quadratic space",
"metabolic quadratic space"
],
[
"group operation",
"group operation"
],
[
"orthogonal",
"orthogonal"
],
[
"direct sum",
"direct sum"
],
[
"algebraic geometry",
"algebraic geometry"
],
[
"variety",
"variety"
],
[
"quotient",
"quotient"
],
[
"Grothendieck group",
"Grothendieck group"
],
[
"isometry",
"isometry"
],
[
"class",
"class"
],
[
"modulo",
"modulo"
],
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"duality",
"duality"
]
],
"raw_glosses": [
"(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"tags": [
"broadly"
],
"topics": [
"algebra",
"algebraic-geometry",
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebraic geometry",
"orig": "en:Algebraic geometry",
"parents": [
"Algebra",
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Category theory",
"orig": "en:Category theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "31 33 35",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "22 40 38",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 35 32",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "33 36 31",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "27 38 34",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "27 38 34",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;\n(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces\n(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.",
"given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces."
],
"id": "en-Witt_group-en-noun-miWU-i82",
"links": [
[
"algebra",
"algebra"
],
[
"field",
"field"
],
[
"characteristic",
"characteristic"
],
[
"abelian group",
"abelian group"
],
[
"equivalence class",
"equivalence class"
],
[
"nondegenerate",
"nondegenerate"
],
[
"symmetric",
"symmetric"
],
[
"bilinear form",
"bilinear form"
],
[
"equivalence relation",
"equivalence relation"
],
[
"metabolic quadratic space",
"metabolic quadratic space"
],
[
"group operation",
"group operation"
],
[
"orthogonal",
"orthogonal"
],
[
"direct sum",
"direct sum"
],
[
"algebraic geometry",
"algebraic geometry"
],
[
"variety",
"variety"
],
[
"quotient",
"quotient"
],
[
"Grothendieck group",
"Grothendieck group"
],
[
"isometry",
"isometry"
],
[
"class",
"class"
],
[
"modulo",
"modulo"
],
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"duality",
"duality"
]
],
"raw_glosses": [
"(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"tags": [
"broadly"
],
"topics": [
"algebra",
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
}
],
"translations": [
{
"_dis1": "31 33 36",
"code": "fr",
"lang": "French",
"sense": "group of equivalence classes found within a field, variety or category",
"tags": [
"masculine"
],
"word": "groupe de Witt"
},
{
"_dis1": "31 33 36",
"code": "de",
"lang": "German",
"sense": "group of equivalence classes found within a field, variety or category",
"tags": [
"feminine"
],
"word": "Witt-Gruppe"
}
],
"wikipedia": [
"Ernst Witt"
],
"word": "Witt group"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with French translations",
"Terms with German translations"
],
"etymology_text": "Named after German mathematician Ernst Witt (1911–1991), who introduced the concept in 1937.",
"forms": [
{
"form": "Witt groups",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Witt group (plural Witt groups)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "Witt decomposition"
},
{
"word": "Witt index"
},
{
"word": "Witt ring"
},
{
"word": "Witt vector"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned",
"en:Algebra",
"en:Algebraic geometry",
"en:Category theory"
],
"examples": [
{
"ref": "1995, Raman Parimala, “Study of quadratic forms - Some connections with geometry”, in S. D. Chatterji, editor, Proceedings of the International Congress of Mathematicians, Zürich m94, Birkhäuser, page 328:",
"text": "A general method of studying the Witt group of a smooth variety is through the graded group associated to the filtration induced by the filtration of the Witt group of the function field by powers of the fundamental ideal of even rank forms.",
"type": "quote"
},
{
"text": "2011, Marco Schlichting, Higher Algebraic K-theory, Guillermo Cortiñas (editor), Topics in Algebraic and Topological K-Theory, Springer, Lecture Notes in Mathematics 2008, page 167,\nThe second reason for this emphasis is that an analog of the Thomason-Waldhausen Localization Theorem also holds for many other (co-) homology theories besides K-theory, among which Hochschild homology, (negative, periodic, ordinary) cyclic homology [49], topological Hochschild (and cyclic) homology [2], triangular Witt groups [6] and higher Grothendieck–Witt groups [77]."
},
{
"ref": "2020, Matthias Wendt, “Oriented Schubert calculus in Chow-Witt rings of Grassmannians”, in Federico Binda, Marc Levine, Manh Toan Nguyen, Oliver Röndigs, editors, Motivic Homotopy Theory and Refined Enumerative Geometry, American Mathematical Society, pages 239–240:",
"text": "The Witt group of a category with duality is given as the quotient of the isometry classes of symmetric spaces modulo metabolic spaces.[…]For coherent and derived Witt groups, the derived tensor product of complexes gives rise to duality-preserving functions and consequently to pairings in triangular Witt groups, cf. [GN03].",
"type": "quote"
}
],
"glosses": [
"Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"links": [
[
"algebra",
"algebra"
],
[
"field",
"field"
],
[
"characteristic",
"characteristic"
],
[
"abelian group",
"abelian group"
],
[
"equivalence class",
"equivalence class"
],
[
"nondegenerate",
"nondegenerate"
],
[
"symmetric",
"symmetric"
],
[
"bilinear form",
"bilinear form"
],
[
"equivalence relation",
"equivalence relation"
],
[
"metabolic quadratic space",
"metabolic quadratic space"
],
[
"group operation",
"group operation"
],
[
"orthogonal",
"orthogonal"
],
[
"direct sum",
"direct sum"
],
[
"algebraic geometry",
"algebraic geometry"
],
[
"variety",
"variety"
],
[
"quotient",
"quotient"
],
[
"Grothendieck group",
"Grothendieck group"
],
[
"isometry",
"isometry"
],
[
"class",
"class"
],
[
"modulo",
"modulo"
],
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"duality",
"duality"
]
],
"raw_glosses": [
"(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned",
"en:Algebra",
"en:Algebraic geometry",
"en:Category theory"
],
"glosses": [
"Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;\n(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces\n(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.",
"given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces"
],
"links": [
[
"algebra",
"algebra"
],
[
"field",
"field"
],
[
"characteristic",
"characteristic"
],
[
"abelian group",
"abelian group"
],
[
"equivalence class",
"equivalence class"
],
[
"nondegenerate",
"nondegenerate"
],
[
"symmetric",
"symmetric"
],
[
"bilinear form",
"bilinear form"
],
[
"equivalence relation",
"equivalence relation"
],
[
"metabolic quadratic space",
"metabolic quadratic space"
],
[
"group operation",
"group operation"
],
[
"orthogonal",
"orthogonal"
],
[
"direct sum",
"direct sum"
],
[
"algebraic geometry",
"algebraic geometry"
],
[
"variety",
"variety"
],
[
"quotient",
"quotient"
],
[
"Grothendieck group",
"Grothendieck group"
],
[
"isometry",
"isometry"
],
[
"class",
"class"
],
[
"modulo",
"modulo"
],
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"duality",
"duality"
]
],
"raw_glosses": [
"(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"tags": [
"broadly"
],
"topics": [
"algebra",
"algebraic-geometry",
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned",
"en:Algebra",
"en:Algebraic geometry",
"en:Category theory"
],
"glosses": [
"Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;\n(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces\n(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.",
"given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces."
],
"links": [
[
"algebra",
"algebra"
],
[
"field",
"field"
],
[
"characteristic",
"characteristic"
],
[
"abelian group",
"abelian group"
],
[
"equivalence class",
"equivalence class"
],
[
"nondegenerate",
"nondegenerate"
],
[
"symmetric",
"symmetric"
],
[
"bilinear form",
"bilinear form"
],
[
"equivalence relation",
"equivalence relation"
],
[
"metabolic quadratic space",
"metabolic quadratic space"
],
[
"group operation",
"group operation"
],
[
"orthogonal",
"orthogonal"
],
[
"direct sum",
"direct sum"
],
[
"algebraic geometry",
"algebraic geometry"
],
[
"variety",
"variety"
],
[
"quotient",
"quotient"
],
[
"Grothendieck group",
"Grothendieck group"
],
[
"isometry",
"isometry"
],
[
"class",
"class"
],
[
"modulo",
"modulo"
],
[
"category theory",
"category theory"
],
[
"category",
"category"
],
[
"duality",
"duality"
]
],
"raw_glosses": [
"(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;"
],
"tags": [
"broadly"
],
"topics": [
"algebra",
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
}
],
"translations": [
{
"code": "fr",
"lang": "French",
"sense": "group of equivalence classes found within a field, variety or category",
"tags": [
"masculine"
],
"word": "groupe de Witt"
},
{
"code": "de",
"lang": "German",
"sense": "group of equivalence classes found within a field, variety or category",
"tags": [
"feminine"
],
"word": "Witt-Gruppe"
}
],
"wikipedia": [
"Ernst Witt"
],
"word": "Witt group"
}
Download raw JSONL data for Witt group meaning in English (9.1kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.