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Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.ContainsIdentities.id_mem

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {W : CategoryTheory.MorphismProperty C}
  [self : W.ContainsIdentities] (X : C), W (CategoryTheory.CategoryStruct.id X)

for all X : C, the identity of X satisfies the morphism property

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

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

CategoryTheory.MorphismProperty.id_mem · cited by 23MorphismProperty.id_memCategoryTheory.Span.id · cited by 4Span.idCategoryTheory.MorphismProperty.ContainsIdentities.sInf · cited by 1ContainsIdentities.sInfCategoryTheory.MorphismProperty.ContainsIdentities.eqToHom · cited by 0ContainsIdentities.eqToHomCategoryTheory.MorphismProperty.ContainsIdentities.iff_identities_le · cited by 0ContainsIdentities.iff_id…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.MorphismProperty.ContainsIdentities · cited by 94MorphismProperty.Contains…ContainsIdentities.id_memCITED BYCITES

Cites4

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

Cited by5

Results whose statement or proof uses this declaration.