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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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 stack 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2011

    started to add to internalization a list of links to examples. Probably we have much more.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2011
    • (edited Jul 5th 2011)

    here is the list of examples of internalization currently listed at internalization:

    Which entries to link to have I still forgotten?

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeJul 5th 2011
    • (edited Jul 5th 2011)

    Why the default first choice of terminology is not chosen uniformly ? I mean if internal groupoid is the default, then internal group would be also default. By the way, I was surprised that the latter was not even a redirect (I added it).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2011

    Why the default first choice of terminology is not chosen uniformly ?

    Because nobody took care to make it uniform when these entries were created over the last years!

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeJul 5th 2011
    • (edited Jul 5th 2011)

    I made some changes to the section on presheaf approach in group object aka internal group, including formulating a proposition. The way it is organized now is pretty confusing, that is why I prefer to have a clear proposition statement and then the rest is kind of proof. But it is a bit strange, e.g. there is a mention of supermanifolds in the proof! Could you look at my changes and see if this can be further improved ? Also did I correctly use the word “creates” in the proposition ?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2011

    Thanks, Zoran, for looking into this.

    I have removed the weird “of supermanifolds”. Clearly this is a leftover of some copy-and-pasting from the discussion of supergroups.

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeJul 7th 2011

    Mostly, it seems that ‘X object’ is for things that are normally just structured sets, while ‘internal X’ is for things that are a bit fancier (higher dimensional in the categorial sense). The distinction on the Lab probably comes from (at least historical, and as far as I know contemporary) practice in the literature.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 13th 2019

    Added a couple more examples.

    diff, v54, current

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)