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Theorems · Theorem · category theory

CategoryTheory.ConcreteCategory.hom_ofHom

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {FC : outParam (C → C → Type u_1)} {CC : outParam (C → Type w)}
  {inst_1 : outParam ((X Y : C) → FunLike (FC X Y) (CC X) (CC Y))} [self : CategoryTheory.ConcreteCategory C FC]
  {X Y : C} (f : FC X Y), CategoryTheory.ConcreteCategory.hom (CategoryTheory.ConcreteCategory.ofHom f) = f
Defined in
Mathlib.CategoryTheory.ConcreteCategory.Basic
Cited by
205 results in Mathlib
Foundations
Depth 5 from the axioms, rests on 13 definitions · uses no axioms
Assumes
CategoryTheory.ConcreteCategory

Around this declaration

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

CategoryTheory.isSheaf_iff_isSheaf_of_type · cited by 30CategoryTheory.isSheaf_if…CategoryTheory.Limits.Types.jointly_surjective_of_isColimit · cited by 27Types.jointly_surjective_…groupHomology.comp_d₂₁_eq · cited by 10groupHomology.comp_d₂₁_eqCommRingCat.isPushout_tensorProduct · cited by 7CommRingCat.isPushout_ten…groupCohomology.comp_d₀₁_eq · cited by 6groupCohomology.comp_d₀₁_…SimplexCategory.mono_iff_injective · cited by 6SimplexCategory.mono_iff_…groupHomology.comp_d₁₀_eq · cited by 6groupHomology.comp_d₁₀_eqgroupHomology.comp_d₃₂_eq · cited by 6groupHomology.comp_d₃₂_eqSimplexCategory.epi_iff_surjective · cited by 5SimplexCategory.epi_iff_s…groupHomology.chainsMap_id_f_hom_eq_mapRange · cited by 5groupHomology.chainsMap_i…groupHomology.d₂₁_single · cited by 5groupHomology.d₂₁_singlegroupHomology.inhomogeneousChains.d_single · cited by 4inhomogeneousChains.d_sin…groupHomology.d₂₁_comp_d₁₀ · cited by 4groupHomology.d₂₁_comp_d₁₀Rep.barComplex.d_single · cited by 3barComplex.d_singleTopCat.induced_of_isLimit · cited by 3TopCat.induced_of_isLimitCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homFunLike · cited by 2560FunLikeCategoryTheory.ConcreteCategory · cited by 421CategoryTheory.ConcreteCa…CategoryTheory.ConcreteCategory.ofHom · cited by 18ConcreteCategory.ofHomConcreteCategory.hom_ofHomCITED BYCITES

Cites5

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Cited by205

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