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Theorems · Definition · category theory

CategoryTheory.SmallCategoryOfSet.id

{Ω : Type w} → (self : CategoryTheory.SmallCategoryOfSet Ω) → (X : ↑self.obj) → ↑(self.hom X X)

identity morphisms

Defined in
Mathlib.CategoryTheory.SmallRepresentatives
Cited by
4 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
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Around this declaration

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

CategoryTheory.SmallCategoryOfSet.id_comp · cited by 0SmallCategoryOfSet.id_compCategoryTheory.SmallCategoryOfSet.id_def · cited by 0SmallCategoryOfSet.id_defCategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id · cited by 0CoreSmallCategoryOfSet.sm…CategoryTheory.SmallCategoryOfSet.comp_id · cited by 0SmallCategoryOfSet.comp_idSet.Elem · cited by 7166Set.ElemCategoryTheory.SmallCategoryOfSet · cited by 11CategoryTheory.SmallCateg…CategoryTheory.SmallCategoryOfSet.obj · cited by 10SmallCategoryOfSet.objCategoryTheory.SmallCategoryOfSet.hom · cited by 6SmallCategoryOfSet.homSmallCategoryOfSet.idCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.