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- Cited by
- 205 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 13 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- FunLikestatement and proof · cited by 2,560
- CategoryTheory.ConcreteCategorystatement and proof · cited by 421
- CategoryTheory.ConcreteCategory.ofHomstatement · cited by 18
Cited by205
Results whose statement or proof uses this declaration.
- CategoryTheory.isSheaf_iff_isSheaf_of_typeproof · cited by 30
- CategoryTheory.Limits.Types.jointly_surjective_of_isColimitproof · cited by 27
- groupHomology.comp_d₂₁_eqproof · cited by 10
- CommRingCat.isPushout_tensorProductproof · cited by 7
- groupCohomology.comp_d₀₁_eqproof · cited by 6
- SimplexCategory.mono_iff_injectiveproof · cited by 6
- groupHomology.comp_d₁₀_eqproof · cited by 6
- groupHomology.comp_d₃₂_eqproof · cited by 6
- SimplexCategory.epi_iff_surjectiveproof · cited by 5
- groupHomology.chainsMap_id_f_hom_eq_mapRangeproof · cited by 5
- groupHomology.d₂₁_singleproof · cited by 5
- groupHomology.inhomogeneousChains.d_singleproof · cited by 4
Showing the 200 most cited of 205.