Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.composePath_mem
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (W : CategoryTheory.MorphismProperty C)
[W.IsMultiplicative] {X Y : C} {p : Quiver.Path X Y}, W.paths p → W (CategoryTheory.composePath p)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.IsMultiplicativestatement and proof · cited by 332
- Quiver.Pathstatement and proof · cited by 166
- CategoryTheory.MorphismProperty.id_memproof · cited by 23
- CategoryTheory.composePathstatement · cited by 16
- CategoryTheory.MorphismProperty.pathsstatement and proof · cited by 13
- CategoryTheory.MorphismProperty.composePath_mem_of_id_memproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_pathsproof · cited by 0
- CategoryTheory.MorphismProperty.paths_le_inverseImageproof · cited by 0