Documentation

Mathlib.Topology.Category.TopCat.EffectiveEpi

Effective epimorphisms in TopCat #

This file proves the result TopCat.effectiveEpi_iff_quotientMap: The effective epimorphisms in TopCat are precisely the quotient maps.

source
noncomputable def TopCat.effectiveEpiStructOfQuotientMap {B : TopCat} {X : TopCat} (π : X ⟶ B) (hπ : QuotientMap ⇑π) :
CategoryTheory.EffectiveEpiStruct π

Implementation: If π is a morphism in TopCat which is a quotient map, then it is an effective epimorphism. The theorem TopCat.effectiveEpi_iff_quotientMap should be used instead of this definition.

Equations
  • One or more equations did not get rendered due to their size.
Instances For
    source
    theorem TopCat.effectiveEpi_iff_quotientMap {B : TopCat} {X : TopCat} (π : X ⟶ B) :
    CategoryTheory.EffectiveEpi π ↔ QuotientMap ⇑π

    The effective epimorphisms in TopCat are precisely the quotient maps.