"categorification" meaning in All languages combined

See categorification on Wiktionary

Noun [English]

Forms: categorifications [plural]
Etymology: category + -fication. Etymology templates: {{suffix|en|category|fication}} category + -fication Head templates: {{en-noun|~}} categorification (countable and uncountable, plural categorifications)
  1. (category theory) A procedure that defines theorems in terms of category theory by mapping concepts from set theory to category theory. Wikipedia link: categorification Tags: countable, uncountable Categories (topical): Category theory Derived forms: decategorification, horizontal categorification, vertical categorification

Inflected forms

Download JSON data for categorification meaning in All languages combined (3.0kB)

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  "etymology_text": "category + -fication.",
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          "word": "decategorification"
        },
        {
          "word": "horizontal categorification"
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          "word": "vertical categorification"
        }
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      "examples": [
        {
          "text": "2008, E. Krenkel, Ramifications of the Geometric Langlands Program, Michael Cowling, Edward Frenkel, Masaki Kashiwara, Alain Valette, David A. Vogan, Jr., Nolan R. Wallach (editors), Representation Theory and Complex Analysis: Lectures Given at the C.I.M.E. Summer School, Springer, Lecture Notes in Mathematics 1931, page 83,\nIn Section 3.4 we have already discussed the question of categorification of the algebra of functions on a homogeneous space like G(F)/K."
        },
        {
          "text": "2009, Volodymyr Mazorchuk, Lectures on sl₂( C )-Modules, Imperial College Press, page 221,\nShow that Φ⊕Φ is also a (naïve) homomorphism of naïve categorifications."
        },
        {
          "ref": "2010, Kishore Marathe, Topics in Physical Mathematics, Springer, page 351",
          "text": "Khovanov's categorification of the Jones polynomial by Khovanov homology is the subject of Section 11.6.",
          "type": "quotation"
        },
        {
          "text": "2011, Robert Wisbauer, Categorical aspects of Hopf algebras, Matilde Marcolli, Deepak Parashar (editors), Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry, Springer Science+Business (Vieweg+Teubner), page 146,\nSince Lawvere's categorification of general algebra, algebras and coalgebras are used as basic notions in universal algebra, logic, and theoretical computer science, for example (e.g. [AdPo], [Gu], [TuPl])."
        }
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        "(category theory) A procedure that defines theorems in terms of category theory by mapping concepts from set theory to category theory."
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          "text": "2008, E. Krenkel, Ramifications of the Geometric Langlands Program, Michael Cowling, Edward Frenkel, Masaki Kashiwara, Alain Valette, David A. Vogan, Jr., Nolan R. Wallach (editors), Representation Theory and Complex Analysis: Lectures Given at the C.I.M.E. Summer School, Springer, Lecture Notes in Mathematics 1931, page 83,\nIn Section 3.4 we have already discussed the question of categorification of the algebra of functions on a homogeneous space like G(F)/K."
        },
        {
          "text": "2009, Volodymyr Mazorchuk, Lectures on sl₂( C )-Modules, Imperial College Press, page 221,\nShow that Φ⊕Φ is also a (naïve) homomorphism of naïve categorifications."
        },
        {
          "ref": "2010, Kishore Marathe, Topics in Physical Mathematics, Springer, page 351",
          "text": "Khovanov's categorification of the Jones polynomial by Khovanov homology is the subject of Section 11.6.",
          "type": "quotation"
        },
        {
          "text": "2011, Robert Wisbauer, Categorical aspects of Hopf algebras, Matilde Marcolli, Deepak Parashar (editors), Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry, Springer Science+Business (Vieweg+Teubner), page 146,\nSince Lawvere's categorification of general algebra, algebras and coalgebras are used as basic notions in universal algebra, logic, and theoretical computer science, for example (e.g. [AdPo], [Gu], [TuPl])."
        }
      ],
      "glosses": [
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      ],
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      ],
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). 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.

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