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nLab > Latest Changes: gaunt category

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJan 22nd 2021

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

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorAlec Rhea
    • CommentTimeMar 3rd 2021

    Added section discussing relation to thin and skeletal categories.

    diff, v5, current

    • 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.

    diff, v6, current

    • CommentRowNumber4.
    • CommentAuthorUlrik
    • CommentTimeMar 3rd 2021

    Corrected the invariant definition.

    diff, v6, current

    • 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.

    diff, v6, current

    • 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.)

    diff, v7, current

  7. examples section copied from univalent category

    Anonymous

    diff, v8, current

  8. definitions copied from univalent category

    Anonymous

    diff, v8, current

    • 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).

    diff, v10, current

    • 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.

    diff, v10, current

    • CommentRowNumber11.
    • CommentAuthorMike Shulman
    • CommentTimeSep 2nd 2022

    A better word for “endoisomorphism” is automorphism.

    diff, v10, current

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

    Anonymous

    diff, v11, current

    • 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
    • CommentTimeSep 18th 2022

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

    diff, v13, current

  15. Add simplex category and Reedy categories as examples of gaunt categories.

    Jonas Frey

    diff, v15, current

  16. Added the category of Archimedean ordered fields and monotonic field homomorphisms to the list of examples - impredicatively this is just the subset of the power set of the real numbers consisting of the Archimedean ordered subfields of the real numbers.

    Peter Wells

    diff, v17, current

    • CommentRowNumber17.
    • CommentAuthorP
    • CommentTimeJun 8th 2025

    merging material from gaunt type into this article into a new section “Gaunt (∞,1)(\infty,1)-categories” since the definition is essentially that of a gaunt category but for (∞,1)(\infty,1)-category.

    diff, v20, current

1 to 17 of 17

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