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Add an example of a cocomplete category without equalizers - #340

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example-cocomplete-no-equalizers
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Add an example of a cocomplete category without equalizers#340
ScriptRaccoon wants to merge 2 commits into
mainfrom
example-cocomplete-no-equalizers

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@ScriptRaccoon

@ScriptRaccoon ScriptRaccoon commented Aug 17, 2026

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Paused since I am on vacation


WIP

This PR adds an example of a cocomplete category without equalizers, namely, the "artificial" example presented in my question MSE/5137415. I have been waiting for answers with other, more natural examples for a while now, but apparently, they just do not exist.

The new category is not just a witness of cocomplete ∧ ¬equalizers, but also of several other property combinations.

TODO. decide all properties if possible. only 1 are currently remaining: effective cocongruences

TODO. when proofs are done, list all property combinations that are new

@ScriptRaccoon
ScriptRaccoon force-pushed the example-cocomplete-no-equalizers branch 6 times, most recently from 311968b to cc45318 Compare August 22, 2026 05:23
@ScriptRaccoon
ScriptRaccoon force-pushed the example-cocomplete-no-equalizers branch from c0a79f5 to 1a9270d Compare August 23, 2026 08:11
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