Not signed in (Sign In)

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 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 infinity 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-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 stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft 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).
  1. This is my first (substantial) contribution to the nLab, so forgive my likely ineptitude. This wants to be a initial stub, everything is basically scraped from the reference and this post: https://golem.ph.utexas.edu/category/2019/07/structured_cospans.html Clearly a lot of material can be added, included a better definition and clearer examples. It’s also quite necessary to make a page for decorated cospans. I might start it myself later this month.

    mattecapu

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 20th 2019

    Just want to say it looks good. Sure, there might be some minor formatting (maybe a sidebar or something, table of contents) to do, but it’s certainly far better than some other newbies.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 20th 2019

    Hi mattecapu,

    could you maybe add an explicit definition of “structured cospan”? As in “A structured cospan is…”.

    Currently the only place where we learn what is meant is only implicit in the third bullet item of the definition of that double category.

    Otherwise there is some grammar to be fixed, various singular/plural issues.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 20th 2019

    Yes, a good start. Are there any standard ways to motivate these constructions?

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJul 20th 2019

    Renamed page to match nLab convention of singular page titles.

    diff, v2, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJul 20th 2019

    I agree that the page is a good start. One suggestion I might make is to start with motivation for the concept in general, rather than only in contrast to decorated cospans; the comparison to decorated cospans could then be a section lower down on the page.

  2. Added an explicit definition of structured cospan.

    mattecapu

    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthormattecapu
    • CommentTimeJul 21st 2019
    Hello everyone,
    I did my best to kick-start the page although I'm actually no expert on this topic, I'm learning-by-contributing this stuff. Hence if someone else has better motivation/definitions for the concept, I'd be happy to read them as well!
    The one I included stems directly from Kenny Courser's talk, where they are basically introduced like this. There might be more in his thesis, so I will look into it.
    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJul 21st 2019

    replaced quiver with directed graph.

    Notice that “quiver” is a concept with an attitude and it’s not the relevant attitude here.

    diff, v5, current

    • CommentRowNumber10.
    • CommentAuthorJoe Moeller
    • CommentTimeNov 16th 2019

    Added a link to the paper Structured Cospans by Baez and Courser.

    diff, v6, current

  3. Reworded to hopefully improve clarity and fluency.

    Mark John Hopkins

    diff, v7, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022
    • (edited Jun 7th 2022)

    I have added the missing “the notion of” in:

    The notion of a structured cospan is a modification of the concept of decorated cospans

    and added the presumeably intended “of decorated cospans” in:

    introduced to provide an improved definition of isomorphism classes of decorated cospans

    \,

    also, I have added floating context menus to the entry

    diff, v8, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    I have added publication data to

    and I will give poor Kenny Courser an author page now, to fix all the broken links to his name requested on this page

    diff, v8, current

    • CommentRowNumber14.
    • CommentAuthorvarkor
    • CommentTime4 days ago

    Remark about the necessity of coproducts.

    diff, v9, current