I have added hyperlinks to the technical terms in the paragraph on flagged categories, starting with “Incidentally” (here).

]]>Nope, that’s wrong. Discrete categories are gaunt, and any surjection of sets between discrete categories is essentially surjective, but for it to be split essentially surjective is exactly AC.

]]>added section on functors and equivalences between gaunt categories.

Anonymous

]]>A better word for “endoisomorphism” is automorphism.

]]>I’m pretty sure all free categories are gaunt, not just those on acyclic graphs. Loops in the graph produce *endomorphisms* in the free category, but not isomorphisms.

Clarified the idea section, and removed the duplicate properties of univalent categories (the reader can just look those up on univalent category).

]]>definitions copied from univalent category

Anonymous

]]>examples section copied from univalent category

Anonymous

]]>Tried to make up for my earlier wrong edits by adding some content on related definitions that are invariant under equivalence. I added the remark that core-thin categories precisely make up the intersection of strict categories and (univalent) categories within the type of flagged categories. (This could perhaps belong somewhere else, however.)

]]>Sorry, I’m confused. I’ve reverted to the previous state. After dinner, I’ll hopefully sort out my confusion, and add back in something correct.

]]>Corrected the invariant definition.

]]>Amended the definition section with the equivalence stable definition. Add a section about univalent foundations: the gaunt categories as the intersection of the strict and the normal/univalent categories (edit: this is false).

I made a link to flagged category, which doesn’t yet exist.

]]>Added section discussing relation to thin and skeletal categories.

]]>Added a remark that the Elephant briefly refers to gaunt categories as “stiff”.

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