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Add properties: core-thin + gaunt#121

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ScriptRaccoon merged 3 commits intomainfrom
gaunt
Apr 22, 2026
Merged

Add properties: core-thin + gaunt#121
ScriptRaccoon merged 3 commits intomainfrom
gaunt

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@ScriptRaccoon ScriptRaccoon commented Apr 22, 2026

This PR adds the two properties "core-thin" and "gaunt" to the database.

A category is core-thin when every automorphism is trivial.
A category is gaunt when every isomorphism is the identity. Equivalently, it is skeletal and core-thin.

As a motivating example, the simplex category is gaunt. With this we can also conceptualize the proof that the simplex category has coquotients of cocongruences (cf. #115): Every core-thin category has this property.

The properties have been decided for all categories in the database. This was an easy task. Also, some previous results on one-way categories have been clarified.

PS: The category of well-ordered sets is a famous example of a core-thin category. But it is not in the database yet.

@ScriptRaccoon ScriptRaccoon force-pushed the gaunt branch 2 times, most recently from ed1982a to 3032a90 Compare April 22, 2026 02:27
@ScriptRaccoon ScriptRaccoon marked this pull request as ready for review April 22, 2026 20:25
@ScriptRaccoon ScriptRaccoon changed the title Add property: gaunt Add properties: core-thin + gaunt Apr 22, 2026
@ScriptRaccoon ScriptRaccoon merged commit 11cc7f0 into main Apr 22, 2026
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@ScriptRaccoon ScriptRaccoon deleted the gaunt branch April 22, 2026 22:50
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