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Theorems · Inductive type · category theory

CategoryTheory.Functor.PreservesEffectiveEpis

{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] → CategoryTheory.Functor C D → Prop

A class describing the property of preserving effective epimorphisms.

Defined in
Mathlib.CategoryTheory.EffectiveEpi.Preserves
Cited by
10 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.Functor.regularEpiOfPreserves · cited by 5Functor.regularEpiOfPrese…CategoryTheory.Functor.reflects_preregular · cited by 3Functor.reflects_preregul…CategoryTheory.regularTopology.equalizerCondition_precomp_of_preservesPullback · cited by 1regularTopology.equalizer…CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_induced · cited by 1regularTopology.exists_ef…CategoryTheory.coherentTopology.equivalence' · cited by 0coherentTopology.equivale…CategoryTheory.regularTopology.coverPreserving · cited by 0regularTopology.coverPres…CategoryTheory.regularTopology.eq_induced · cited by 0regularTopology.eq_inducedCategoryTheory.regularTopology.equivalence · cited by 0regularTopology.equivalen…CategoryTheory.Functor.PreservesEffectiveEpis.casesOn · cited by 0PreservesEffectiveEpis.ca…CategoryTheory.Functor.PreservesEffectiveEpis.preserves · cited by 0PreservesEffectiveEpis.pr…CategoryTheory.Functor.PreservesEffectiveEpis.recOn · cited by 0PreservesEffectiveEpis.re…CategoryTheory.Functor.regularEpiOfPreserves_W · cited by 0Functor.regularEpiOfPrese…CategoryTheory.Functor.regularEpiOfPreserves_isColimit · cited by 0Functor.regularEpiOfPrese…CategoryTheory.Functor.regularEpiOfPreserves_left · cited by 0Functor.regularEpiOfPrese…CategoryTheory.Functor.regularEpiOfPreserves_right · cited by 0Functor.regularEpiOfPrese…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorFunctor.PreservesEffectiveEpisCITED BYCITES

Cites2

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

Cited by15

Results whose statement or proof uses this declaration.