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Theorems · Theorem · category theory

CategoryTheory.Functor.ReflectsEffectiveEpis.reflects

∀ {C : Type u_1} {inst : CategoryTheory.Category.{v_1, u_1} C} {D : Type u_2}
  {inst_1 : CategoryTheory.Category.{v_2, u_2} D} {F : CategoryTheory.Functor C D} [self : F.ReflectsEffectiveEpis]
  {X Y : C} (f : X ⟶ Y), CategoryTheory.EffectiveEpi (F.map f) → CategoryTheory.EffectiveEpi f

A functor reflects effective epimorphisms if morphisms that are mapped to epimorphisms are themselves effective epimorphisms.

Defined in
Mathlib.CategoryTheory.EffectiveEpi.Preserves
Cited by
1 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.Functor.ReflectsEffectiveEpis
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CategoryTheory.Functor.effectiveEpi_of_map · cited by 2Functor.effectiveEpi_of_m…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.EffectiveEpi · cited by 86CategoryTheory.EffectiveE…CategoryTheory.Functor.ReflectsEffectiveEpis · cited by 6Functor.ReflectsEffective…ReflectsEffectiveEpis.reflectsCITED BYCITES

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