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 beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory 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 elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory 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 homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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-theory subobject 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).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeDec 19th 2017

    Created a stubby poset-valued set.

    • CommentRowNumber2.
    • CommentAuthormaxsnew
    • CommentTimeDec 19th 2017
    • (edited Dec 19th 2017)

    Looks like a comma double category from FF to PP. Objects are functions FAPF A \to P and horizontal morphisms are squares from some FR:FAFBF R : F A \nrightarrow F B to P\leq_P along those functions. Then you should have vertical arrows which are of the form FfF f and make a commutative triangle and some kind of squares. I’m not very familiar with models of linear logic though so I don’t know if those notion already has a name for coherence spaces.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeDec 19th 2017

    That was exactly my thought on reading it!! There ought to be a general theory of when comma double categories inherit structure from their inputs. Comma double categories have also been used recently to induce structure on decorated cospans, and I believe that some forms of the Dialectica construction can also be represented as comma double categories. However, I don’t have time to think about this any more right now.

    • CommentRowNumber4.
    • CommentAuthormaxsnew
    • CommentTimeFeb 9th 2018

    Just found mention of “HH-valued sets” on the tripos page. Are they the same? They look very similar.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 10th 2018

    They do look somewhat similar, but I don’t think they’re the same. There are no symmetry or transitivity requirements, and the morphisms between them are different.