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Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.prop_of_retract

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C) [P.IsStableUnderRetracts]
  {X Y : C} (h : CategoryTheory.Retract X Y), P Y → P X
Defined in
Mathlib.CategoryTheory.ObjectProperty.Retract
Cited by
2 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.ObjectProperty.IsStableUnderRetracts
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Around this declaration

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CategoryTheory.ObjectProperty.retractClosure_eq_self · cited by 6ObjectProperty.retractClo…CategoryTheory.InternallyProjective.ofRetract · cited by 0InternallyProjective.ofRe…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…CategoryTheory.Retract · cited by 34CategoryTheory.RetractCategoryTheory.ObjectProperty.IsStableUnderRetracts · cited by 12ObjectProperty.IsStableUn…CategoryTheory.ObjectProperty.IsStableUnderRetracts.of_retract · cited by 5IsStableUnderRetracts.of_…ObjectProperty.prop_of_retractCITED BYCITES

Cites5

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Cited by2

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