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Theorems · Definition · category theory

CommGrpCat.coyonedaType

CategoryTheory.Functor Type uᵒᵖ (CategoryTheory.Functor CommGrpCat CommGrpCat)

The Hom bifunctor sending a type X and a commutative group G to the commutative group X → G with pointwise operations. This is also the coyoneda embedding of Type into CommGrpCat-valued presheaves of commutative groups.

Defined in
Mathlib.Algebra.Category.Grp.Yoneda
Cited by
3 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CommGrpCat.coyonedaType_map_app · cited by 0CommGrpCat.coyonedaType_m…CommGrpCat.coyonedaType_obj_map · cited by 0CommGrpCat.coyonedaType_o…CommGrpCat.coyonedaType_obj_obj_coe · cited by 0CommGrpCat.coyonedaType_o…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homOpposite.unop · cited by 2231Opposite.unopQuiver.Hom.unop · cited by 903Hom.unopMonoidHom.comp · cited by 469MonoidHom.compCommGrpCat · cited by 74CommGrpCatCommGrpCat.carrier · cited by 59CommGrpCat.carrierCommGrpCat.of · cited by 28CommGrpCat.ofCommGrpCat.Hom.hom · cited by 26Hom.homCommGrpCat.ofHom · cited by 19CommGrpCat.ofHomPi.evalMonoidHom · cited by 14Pi.evalMonoidHomMonoidHom.pi · cited by 9MonoidHom.piCommGrpCat.coyonedaTypeCITED BYCITES

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.