Theorems · Theorem · category theory
CategoryTheory.eqToHom_trans
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} (p : X = Y) (q : Y = Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom p) (CategoryTheory.eqToHom q) = CategoryTheory.eqToHom ⋯- Defined in
- Mathlib.CategoryTheory.EqToHom
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.eqToHomstatement · cited by 860
Cited by54
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.ext_of_isoproof · cited by 28
- CategoryTheory.eqToHom_trans_assocproof · cited by 25
- CategoryTheory.ComposableArrows.ext₁proof · cited by 16
- TopCat.Sheaf.eq_of_locally_eq'proof · cited by 6
- CategoryTheory.Paths.ext_functorproof · cited by 6
- CategoryTheory.ComposableArrows.ext_succproof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invAppproof · cited by 5
- CategoryTheory.Pseudofunctor.mapComp'_comp_idproof · cited by 4
- CategoryTheory.Pseudofunctor.mapComp'_id_compproof · cited by 4
- CategoryTheory.constant_of_preserves_morphismsproof · cited by 3
- HomologicalComplex.XIsoOfEq_hom_comp_XIsoOfEq_homproof · cited by 2
- AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen'proof · cited by 2