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Mathlib.Topology.Category.LightProfinite.EffectiveEpi

Effective epimorphisms in LightProfinite #

This file proves that EffectiveEpi and Surjective are equivalent in LightProfinite. As a consequence we deduce from the material in Mathlib.Topology.Category.CompHausLike.EffectiveEpi that LightProfinite is Preregular and Precoherent.

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theorem LightProfinite.effectiveEpi_iff_surjective {X : LightProfinite} {Y : LightProfinite} (f : X ⟶ Y) :
CategoryTheory.EffectiveEpi f ↔ Function.Surjective ⇑f
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instance LightProfinite.instPreregular :
CategoryTheory.Preregular LightProfinite
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