Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_paths
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (W : CategoryTheory.MorphismProperty C),
W.multiplicativeClosure = W.paths.strictMap (CategoryTheory.pathComposition C)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites18
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.Functor.objproof · cited by 19,642
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- le_antisymmproof · cited by 2,068
- CategoryTheory.Pathsstatement · cited by 82
- Quiver.Hom.toPathproof · cited by 38
- CategoryTheory.MorphismProperty.strictMapstatement and proof · cited by 23
- CategoryTheory.MorphismProperty.multiplicativeClosurestatement and proof · cited by 18
- CategoryTheory.MorphismProperty.pathsstatement and proof · cited by 13
- CategoryTheory.pathCompositionstatement and proof · cited by 9
- CategoryTheory.MorphismProperty.le_multiplicativeClosureproof · cited by 6
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