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Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.Respects

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

A morphism property P satisfies P.Respects Q if it is stable under composition on the left and right by morphisms satisfying Q.

Defined in
Mathlib.CategoryTheory.MorphismProperty.Basic
Cited by
2 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryStruct
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.MorphismProperty.RespectsIso · cited by 248MorphismProperty.Respects…AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally · cited by 3HasRingHomProperty.iff_ex…AlgebraicGeometry.HasRingHomProperty.respects_isOpenImmersion · cited by 1HasRingHomProperty.respec…CategoryTheory.MorphismProperty.IsLocalAtTarget.recOn · cited by 0IsLocalAtTarget.recOnCategoryTheory.MorphismProperty.IsLocalAtSource.casesOn · cited by 0IsLocalAtSource.casesOnCategoryTheory.MorphismProperty.IsLocalAtSource.recOn · cited by 0IsLocalAtSource.recOnCategoryTheory.MorphismProperty.IsLocalAtTarget.casesOn · cited by 0IsLocalAtTarget.casesOnCategoryTheory.MorphismProperty.Respects.casesOn · cited by 0Respects.casesOnCategoryTheory.MorphismProperty.Respects.recOn · cited by 0Respects.recOnCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…MorphismProperty.RespectsCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.