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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeJan 22nd 2021

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

• CommentRowNumber2.
• CommentAuthorAlec Rhea
• CommentTimeMar 3rd 2021

Added section discussing relation to thin and skeletal categories.

• CommentRowNumber3.
• CommentAuthorUlrik
• CommentTimeMar 3rd 2021
• (edited Mar 4th 2021)

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.

• CommentRowNumber4.
• CommentAuthorUlrik
• CommentTimeMar 3rd 2021

Corrected the invariant definition.

• CommentRowNumber5.
• CommentAuthorUlrik
• CommentTimeMar 3rd 2021

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.

• CommentRowNumber6.
• CommentAuthorUlrik
• CommentTimeMar 3rd 2021

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.)

1. examples section copied from univalent category

Anonymous

2. definitions copied from univalent category

Anonymous

• CommentRowNumber9.
• CommentAuthorMike Shulman
• CommentTimeSep 2nd 2022

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

• CommentRowNumber10.
• CommentAuthorMike Shulman
• CommentTimeSep 2nd 2022

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.

• CommentRowNumber11.
• CommentAuthorMike Shulman
• CommentTimeSep 2nd 2022

A better word for “endoisomorphism” is automorphism.

3. added section on functors and equivalences between gaunt categories.

Anonymous

• CommentRowNumber13.
• CommentAuthorMike Shulman
• CommentTimeSep 3rd 2022

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.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTime7 days ago

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

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