Theorems · Theorem · category theory
CategoryTheory.composePath_toPath
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y),
CategoryTheory.composePath f.toPath = f- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Category.id_compproof · cited by 1,998
- Quiver.Hom.toPathstatement · cited by 38
- CategoryTheory.composePathstatement · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.Construction.facproof · cited by 3
- CategoryTheory.Quiv.freeMap_pathsOf_pathCompositionproof · cited by 0
- CategoryTheory.ReflQuiv.adj.counit.comp_app_eqproof · cited by 0
- CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_pathsproof · cited by 0
- CategoryTheory.Quiv.pathComposition_naturalityproof · cited by 0