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Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.multiplicativeClosure

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty C

Given a morphism property W, the multiplicativeClosure W is the smallest multiplicative property greater than or equal to W.

Defined in
Mathlib.CategoryTheory.MorphismProperty.Composition
Cited by
18 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MorphismProperty.le_multiplicativeClosure · cited by 6MorphismProperty.le_multi…SimplexCategoryGenRel.P_σ · cited by 5SimplexCategoryGenRel.P_σSimplexCategoryGenRel.P_δ · cited by 5SimplexCategoryGenRel.P_δCategoryTheory.MorphismProperty.multiplicativeClosure_le_iff · cited by 4MorphismProperty.multipli…SimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_top · cited by 2SimplexCategoryGenRel.mul…CategoryTheory.Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMk · cited by 2FreeRefl.multiplicativeCl…SimplexCategoryGenRel.hom_induction · cited by 1SimplexCategoryGenRel.hom…CategoryTheory.MorphismProperty.strictMap_multiplicativeClosure_le · cited by 1MorphismProperty.strictMa…SSet.Truncated.HomotopyCategory.multiplicativeClosure_morphismPropertyHomMk · cited by 1HomotopyCategory.multipli…CategoryTheory.MorphismProperty.multiplicativeClosure.below · cited by 1multiplicativeClosure.bel…CategoryTheory.MorphismProperty.multiplicativeClosure.casesOn · cited by 1multiplicativeClosure.cas…CategoryTheory.MorphismProperty.multiplicativeClosure_eq_multiplicativeClosure' · cited by 1MorphismProperty.multipli…CategoryTheory.MorphismProperty.multiplicativeClosure_eq_self · cited by 1MorphismProperty.multipli…SimplexCategoryGenRel.eq_or_len_le_of_P_δ · cited by 0SimplexCategoryGenRel.eq_…SimplexCategoryGenRel.exists_P_σ_P_δ_factorization · cited by 0SimplexCategoryGenRel.exi…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…MorphismProperty.multiplicati…CITED BYCITES

Cites2

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Cited by24

Results whose statement or proof uses this declaration.