Effective epimorphisms in TopCat

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

noncomputable def TopCat.effectiveEpiStructOfQuotientMap {B : TopCat} {X : TopCat} (π : X ⟶ B) (hπ : IsQuotientMap ⇑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_isQuotientMap should be used instead of this definition.

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theorem TopCat.effectiveEpi_iff_isQuotientMap {B : TopCat} {X : TopCat} (π : X ⟶ B) : CategoryTheory.EffectiveEpi π ↔ IsQuotientMap ⇑π

The effective epimorphisms in TopCat are precisely the quotient maps.

@[deprecated TopCat.effectiveEpi_iff_isQuotientMap]

theorem TopCat.effectiveEpi_iff_quotientMap {B : TopCat} {X : TopCat} (π : X ⟶ B) : CategoryTheory.EffectiveEpi π ↔ IsQuotientMap ⇑π

Alias of TopCat.effectiveEpi_iff_isQuotientMap.

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The effective epimorphisms in TopCat are precisely the quotient maps.