Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: gaunt category

Bottom of Page

1 to 15 of 15

  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

1 to 15 of 15

  1.  
Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.

    • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)
 
Back to Discussions Top of Page