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Theorems · Definition · category theory

CategoryTheory.Retract.refl

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → (X : C) → CategoryTheory.Retract X X

Any object is a retract of itself.

Defined in
Mathlib.CategoryTheory.Retract
Cited by
3 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.ObjectProperty.le_retractClosure · cited by 5ObjectProperty.le_retract…CategoryTheory.Retract.refl_i · cited by 0Retract.refl_iCategoryTheory.Retract.refl_r · cited by 0Retract.refl_rCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Retract · cited by 34CategoryTheory.RetractRetract.reflCITED BYCITES

Cites3

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

Cited by3

Results whose statement or proof uses this declaration.