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 bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics 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 finite 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 internal-categories k-theory lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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 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.
    • CommentAuthorPeter Heinig
    • CommentTimeJul 3rd 2017

    Added a literature reference to icon. Started some systematic notes on icons for monoidal-enriched bicategories, which I am currently using for something. Think the broken-off state of that section is not intolerable, in particular since I have seen similar work in progress on the nLab. Intend to continue them soon.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJul 4th 2017

    I don’t think that this is the place to recall the definition of enriched functor of bicategories.

    • CommentRowNumber3.
    • CommentAuthorPeter Heinig
    • CommentTimeJul 4th 2017

    I don’t think that this is the place to recall the definition of enriched functor of bicategories.

    Removed it.

    Is there a place on the nLab where an exposition of parts of, and material related to, the article Adv. Math. 289, 1–94, would fit? (There are detailed expository parts of the nLab; for bicategories and string diagrams there appear not to be detailed nLab expositions yet.)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJul 5th 2017

    Well, there’s room for quite a lot more at enriched bicategory. The definition of enriched icon could certainly go at icon. If you want to write a lot about functors, it could go on a new page like enriched pseudofunctor. A small amount about the relevant kind of limits could be included at 2-limit, or if you want to write a lot then maybe it would be worth having its own page like enriched 2-limit or something. If you want to write about the tricategory of enriched modules, you could maybe create 2-profunctor. (On the nLab I believe the usual convention is still that, contrary to much of the literature, the prefix “2-” doesn’t imply strictness, only 2-dimensionality, thereby avoiding the need for words like “bilimit”.) The second half of the paper could maybe go at profunctor or proarrow equipment, or perhaps we could go for the new naming-pages-after-theorems convention and make enriched categories, functors, and profunctors are a free cocompletion. There are other possibilities as well.

    • CommentRowNumber5.
    • CommentAuthorPeter Heinig
    • CommentTimeJul 5th 2017
    • (edited Jul 5th 2017)

    Very helpful answer, many thanks.

    Especially with

    (On the nLab I believe the usual convention is still that, contrary to much of the literature, the prefix “2-” doesn’t imply strictness, only 2-dimensionality, thereby avoiding the need for words like “bilimit”.)

    you preempted a question of mine (I had taken care to use the “bi”-prefix in the planned page on icons, since the plan was and is to better learn and document the constructions for weak 2-categories, and then was surprised that the usage was edited back to the “2-” convention).

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)