Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.multiplicativeClosure_le_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W W' : CategoryTheory.MorphismProperty C)
[W'.IsMultiplicative], W.multiplicativeClosure ≤ W' ↔ W ≤ W'The multiplicative closure of W is the smallest multiplicative property greater than or equal
to W.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LE.le.transproof · cited by 3,151
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.IsMultiplicativestatement and proof · cited by 332
- CategoryTheory.MorphismProperty.comp_memproof · cited by 48
- CategoryTheory.MorphismProperty.id_memproof · cited by 23
- CategoryTheory.MorphismProperty.multiplicativeClosurestatement and proof · cited by 18
- CategoryTheory.MorphismProperty.le_multiplicativeClosureproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- SSet.Truncated.HomotopyCategory.morphismProperty_eq_topproof · cited by 0
- CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_pathsproof · cited by 0
- CategoryTheory.Cat.FreeRefl.morphismProperty_eq_topproof · cited by 0