Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.comp_mem_paths_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W : CategoryTheory.MorphismProperty C} {X Y Z : C}
{p : Quiver.Path X Y} {q : Quiver.Path Y Z}, W.paths (p.comp q) ↔ W.paths p ∧ W.paths q- 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.
Cites7
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.Homproof · cited by 32,603
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.compstatement and proof · cited by 45
- CategoryTheory.MorphismProperty.pathsstatement and proof · cited by 13
- Quiver.Path.comp_consproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.comp_mem_paths_iff'proof · cited by 0