Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.le_multiplicativeClosure
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W : CategoryTheory.MorphismProperty C),
W ≤ W.multiplicativeClosureThe multiplicative closure is greater than or equal to the original property.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- 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.Homproof · cited by 32,603
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.multiplicativeClosurestatement · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.multiplicativeClosure_le_iffproof · cited by 4
- CategoryTheory.Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMkproof · cited by 2
- CategoryTheory.MorphismProperty.multiplicativeClosure_eq_selfproof · cited by 1
- CategoryTheory.MorphismProperty.strictMap_multiplicativeClosure_leproof · cited by 1
- CategoryTheory.MorphismProperty.multiplicativeClosure_eq_strictMap_pathsproof · cited by 0
- CategoryTheory.MorphismProperty.multiplicativeClosure_monotoneproof · cited by 0