Theorems · Definition · category theory
CategoryTheory.composePath
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → Quiver.Path X Y → (X ⟶ Y)A path in a category can be composed to a single morphism.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.brecOnproof · cited by 10
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.pathCompositionproof · cited by 9
- CategoryTheory.composePath_toPathstatement · cited by 5
- CategoryTheory.Quiv.liftproof · cited by 2
- CategoryTheory.MorphismProperty.composePath_memstatement · cited by 2
- CategoryTheory.pathComposition_mapstatement · cited by 1
- CategoryTheory.MorphismProperty.composePath_mem_of_id_memstatement and proof · cited by 1
- CategoryTheory.composePath_compstatement and proof · cited by 1
- CategoryTheory.Quiv.lift_mapstatement · cited by 0
- CategoryTheory.composePath.eq_defstatement and proof · cited by 0
- CategoryTheory.Groupoid.vertexGroupIsomOfPathproof · cited by 0
- CategoryTheory.MorphismProperty.composePath_mem_of_length_posstatement and proof · cited by 0
- CategoryTheory.composePath_comp'statement · cited by 0