Theorems · Theorem · category theory
CategoryTheory.pathComposition_map
∀ (C : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : CategoryTheory.Paths C} (f : X ⟶ Y),
(CategoryTheory.pathComposition C).map f = CategoryTheory.composePath f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 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 and proof · cited by 32,603
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Pathsstatement and proof · cited by 82
- CategoryTheory.composePathstatement · cited by 16
- CategoryTheory.pathCompositionstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_pathsproof · cited by 0