Theorems · Theorem · category theory
CategoryTheory.Arrow.Hom.w
∀ {T : Type u} [inst : CategoryTheory.Category.{v, u} T] {f g : CategoryTheory.Arrow T} (sq : f ⟶ g),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Arrow.Hom.left sq) g.hom =
CategoryTheory.CategoryStruct.comp f.hom (CategoryTheory.Arrow.Hom.right sq)Alias of CategoryTheory.Arrow.w.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.Arrow.leftstatement · cited by 426
- CategoryTheory.Arrow.rightstatement · cited by 423
- CategoryTheory.Arrow.homstatement · cited by 335
- CategoryTheory.Arrow.Hom.rightstatement · cited by 176
- CategoryTheory.Arrow.Hom.leftstatement · cited by 160
- CategoryTheory.Arrow.wproof · cited by 7
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.Arrow.w_mk_rightproof · cited by 13
- CategoryTheory.Pretriangulated.exists_iso_of_arrow_isoproof · cited by 2
- CategoryTheory.RetractArrow.i_wproof · cited by 2
- CategoryTheory.SmallObject.ιFunctorObj_eqproof · cited by 1
- CategoryTheory.Arrow.w_mkproof · cited by 1
- CategoryTheory.Arrow.w_mk_leftproof · cited by 1
- CategoryTheory.SmallObject.πFunctorObj_eqproof · cited by 1
- CategoryTheory.SmallObject.πObj_naturalityproof · cited by 1
- CategoryTheory.RetractArrow.r_wproof · cited by 1
- CategoryTheory.Functor.mem_mapTriangle_essImage_of_distinguishedproof · cited by 1
- CategoryTheory.Arrow.Hom.w_assocproof · cited by 0