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 bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity 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 internal-categories k-theory lie lie-theory limit 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 nonassociative 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory 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.
    • CommentAuthorSam Staton
    • CommentTimeJan 3rd 2018

    After this discussion at string diagrams for linearly distributive categories with unit = counit, I finally got round to having a go at making star-polycategory. Still much more to do. Hopefully I didn’t make any major mistakes so far.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeJan 3rd 2018

    Looks great to me, thanks! Two comments:

    • When creating a new page, it’s a good idea to make links to it from all reasonable related pages so that people can find it. This sometimes requires a little thought as to where on such pages to put the link, perhaps making a new section somewhere for a few sentence discussion of the relationship, or if the relationship isn’t that important it can just be linked without explanation in the “Related pages” section. In this case it would be good to have links at least from star-autonomous category and polycategory, and maybe other places such as cyclic multicategory (oops, that doesn’t exist yet either, but we have cyclic operad). Would you like to try adding some links?

    • It would be nice to actually have a precise definition of the compatibility conditions between composition and the exchange/negation structure. Are these axioms actually written down anywhere, or does everyone always just say “they’re obvious”? If the latter, maybe we can remedy that situation by working out what they should be.

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeJan 4th 2018

    Thanks Mike. I added some links for star-autonomous categories and polycategories. I am not quite sure how to make the link from cyclic multicategories. I agree it would be good to work out the compatibility conditions.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJan 5th 2018

    Looks good, thanks. For the plural link star-polycategories (which you wrote at polycategory) to work, you need to add

    [[!redirects star-polycategories]]
    

    to the bottom of the page star-polycategory. Probably it would be good to also redirect other spellings like *-polycategory and *-polycategories.

    To make a link from cyclic multicategory someone would have to first create the page cyclic multicategory. I don’t have time to do that now, but anyone who wants to could just make a stub to record links.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJan 30th 2018

    I added to star-polycategory a bit more detail about what I think the compatibility conditions should be.