"group functor" meaning in English

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  "pos": "noun",
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          "langcode": "en",
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        {
          "ref": "1972, A. K. Bousfield, D. M. Kan, Homotopy Limits, Completions and Localizations, Springer, page 106",
          "text": "In order to be able to efficiently state the main results of this chapter (in §4) we formulate here a group-functor version of the R-nilpotent tower lemma (Ch.III, 6.4).",
          "type": "quotation"
        },
        {
          "ref": "2003, Jens Carsten Jantzen, Representations of Algebraic Groups, 2nd edition, American Mathematical Society, page 20",
          "text": "A direct product of k–group functors is again a k–group functor; so is a fibre product if the morphisms used in its construction are homomorphisms of k–group functors.",
          "type": "quotation"
        },
        {
          "ref": "2017, J. S. Milne, Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field, Cambridge University Press, page 118",
          "text": "By a group functor we mean a functor from small k-algebras to groups. A homomorphism of group functors is a natural transformation. A subgroup functor of a group functor G is a subfunctor H such that H(R) is a subgroup of G(R) for all R; it is normal if H(R) is normal in G(R) for all R.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group."
      ],
      "id": "en-group_functor-en-noun-GVfEnkJR",
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          "category theory",
          "category theory"
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          "algebraic geometry",
          "algebraic geometry"
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        [
          "group object",
          "group object"
        ],
        [
          "object",
          "object"
        ],
        [
          "category",
          "category"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "group",
          "group"
        ]
      ],
      "raw_glosses": [
        "(category theory, algebraic geometry) A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group."
      ],
      "related": [
        {
          "word": "subgroup functor"
        }
      ],
      "topics": [
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        "category-theory",
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        "engineering",
        "geometry",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
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    }
  ],
  "word": "group functor"
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      "word": "subgroup functor"
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          "ref": "1972, A. K. Bousfield, D. M. Kan, Homotopy Limits, Completions and Localizations, Springer, page 106",
          "text": "In order to be able to efficiently state the main results of this chapter (in §4) we formulate here a group-functor version of the R-nilpotent tower lemma (Ch.III, 6.4).",
          "type": "quotation"
        },
        {
          "ref": "2003, Jens Carsten Jantzen, Representations of Algebraic Groups, 2nd edition, American Mathematical Society, page 20",
          "text": "A direct product of k–group functors is again a k–group functor; so is a fibre product if the morphisms used in its construction are homomorphisms of k–group functors.",
          "type": "quotation"
        },
        {
          "ref": "2017, J. S. Milne, Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field, Cambridge University Press, page 118",
          "text": "By a group functor we mean a functor from small k-algebras to groups. A homomorphism of group functors is a natural transformation. A subgroup functor of a group functor G is a subfunctor H such that H(R) is a subgroup of G(R) for all R; it is normal if H(R) is normal in G(R) for all R.",
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        "A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
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          "algebraic geometry",
          "algebraic geometry"
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        [
          "group object",
          "group object"
        ],
        [
          "object",
          "object"
        ],
        [
          "category",
          "category"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "group",
          "group"
        ]
      ],
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        "(category theory, algebraic geometry) A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group."
      ],
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        "engineering",
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  "word": "group functor"
}