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Theorems · Definition · category theory

CategoryTheory.Iso.retract

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

If X is isomorphic to Y, then X is a retract of Y.

Defined in
Mathlib.CategoryTheory.Retract
Cited by
4 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.hasInjectiveDimensionLT_of_iso · cited by 1CategoryTheory.hasInjecti…CategoryTheory.hasProjectiveDimensionLT_of_iso · cited by 1CategoryTheory.hasProject…CategoryTheory.Iso.retract_r · cited by 0Iso.retract_rCategoryTheory.Iso.retract_i · cited by 0Iso.retract_iCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Retract · cited by 34CategoryTheory.RetractIso.retractCITED BYCITES

Cites5

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.