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Theorems · Theorem · category theory

CategoryTheory.Equivalence.map_injective_iff

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u_1}
  [inst_1 : CategoryTheory.Category.{v_1, u_1} D] (F : C ≌ D) (P : C),
  CategoryTheory.Injective (F.functor.obj P) ↔ CategoryTheory.Injective P
Defined in
Mathlib.CategoryTheory.Preadditive.Injective.Basic
Cited by
1 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category
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Around this declaration

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

AddCommGrpCat.injective_as_module_iff · cited by 0AddCommGrpCat.injective_a…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Equivalence.functor · cited by 1268Equivalence.functorCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.Equivalence.symm · cited by 195Equivalence.symmCategoryTheory.Injective · cited by 70CategoryTheory.InjectiveCategoryTheory.Equivalence.toAdjunction · cited by 60Equivalence.toAdjunctionCategoryTheory.Adjunction.map_injective · cited by 2Adjunction.map_injectiveCategoryTheory.Adjunction.injective_of_map_injective · cited by 1Adjunction.injective_of_m…Equivalence.map_injective_iffCITED BYCITES

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