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Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.sourceLocalClosure

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

The source-local closure of P along a precoverage K is the weakest property containing P that is local on the source.

Defined in
Mathlib.CategoryTheory.MorphismProperty.LocalClosure
Cited by
4 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.MorphismProperty.sourceLocalClosure.below · cited by 1sourceLocalClosure.belowCategoryTheory.MorphismProperty.sourceLocalClosure.brecOn · cited by 0sourceLocalClosure.brecOnCategoryTheory.MorphismProperty.sourceLocalClosure.casesOn · cited by 0sourceLocalClosure.casesOnCategoryTheory.MorphismProperty.sourceLocalClosure.le · cited by 0sourceLocalClosure.leCategoryTheory.MorphismProperty.sourceLocalClosure.le_of_isLocalAtSource · cited by 0sourceLocalClosure.le_of_…CategoryTheory.MorphismProperty.sourceLocalClosure.below.casesOn · cited by 0below.casesOnCategoryTheory.MorphismProperty.sourceLocalClosure.recOn · cited by 0sourceLocalClosure.recOnCategoryTheory.MorphismProperty.sourceLocalClosure.sourceLocalClosure_iff_of_respectsLeft · cited by 0sourceLocalClosure.source…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Precoverage · cited by 204CategoryTheory.PrecoverageMorphismProperty.sourceLocalC…CITED BYCITES

Cites3

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Cited by8

Results whose statement or proof uses this declaration.