Theorems · Theorem · category theory
CategoryTheory.composePath_comp
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} (f : Quiver.Path X Y) (g : Quiver.Path Y Z),
CategoryTheory.composePath (f.comp g) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.composePath f) (CategoryTheory.composePath g)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.comp_idproof · cited by 2,119
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.compstatement and proof · cited by 45
- CategoryTheory.composePathstatement and proof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.composePath_comp'proof · cited by 0