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Existence of reflexive coequalizers#36

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ScriptRaccoon merged 2 commits intomainfrom
existence-reflexive-coequalizers
Apr 6, 2026
Merged

Existence of reflexive coequalizers#36
ScriptRaccoon merged 2 commits intomainfrom
existence-reflexive-coequalizers

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@ScriptRaccoon ScriptRaccoon commented Apr 6, 2026

This PR adds a little lemma: If a category has binary products and coreflexive equalizers, then it has equalizers. As usual, this implication is dualized automatically.

This lemma in particular shows that the category of manifolds does not have coreflexive equalizers and reflexive coequalizers.

I also documented the decision (which has been done long ago, but it was never written down) that the implications are preferred in their "limit" variant.

@ScriptRaccoon ScriptRaccoon force-pushed the existence-reflexive-coequalizers branch from 73022e4 to a2dc794 Compare April 6, 2026 10:21
@ScriptRaccoon ScriptRaccoon merged commit 520f42a into main Apr 6, 2026
@ScriptRaccoon ScriptRaccoon deleted the existence-reflexive-coequalizers branch April 6, 2026 21:25
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