Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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 sheaves 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

1. • CommentRowNumber1.
   • CommentAuthorJames
   • CommentTimeAug 22nd 2020
   • (edited Aug 22nd 2020)
   • PermaLink
   Author: James
   Format: MarkdownItexCould categories be considered generalized uniform structures, extending [[generalized uniform structures - table|this table]] by the following row? - proarrow -> directed graph - monad -> category - pro-monad -> ? - symmetric proarrow -> undirected graph - symmetric monad -> groupoid - symmetric pro-monad -> ?

   Could categories be considered generalized uniform structures, extending this table by the following row?

   • proarrow -> directed graph
   • monad -> category
   • pro-monad -> ?
   • symmetric proarrow -> undirected graph
   • symmetric monad -> groupoid
   • symmetric pro-monad -> ?
2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeAug 23rd 2020
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCertainly there is such a row. I'm not sure I'd be inclined to consider a category to be a generalized uniform structure though, rather I would just say that both are an instance of a monad in a bicategory (or perhaps a bit more specifically a [[generalized multicategory]]). I'd forgotten the existence of this table. On which pages is it included?

   Certainly there is such a row. I’m not sure I’d be inclined to consider a category to be a generalized uniform structure though, rather I would just say that both are an instance of a monad in a bicategory (or perhaps a bit more specifically a generalized multicategory).

   I’d forgotten the existence of this table. On which pages is it included?

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeAug 23rd 2020
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexIt\'s the pro-monads that are generalized uniform structures, not the monads themselves. Algebraic geometers seem to study pro-groupoids (which are to pro-groups as groupoids are to groups), but I haven\'t checked if that\'s really what goes in the last blank. If it does, then they are generalized uniform structures. The table is included in most of the pages that it links to, but not the ones for the simplest concepts.

   It's the pro-monads that are generalized uniform structures, not the monads themselves. Algebraic geometers seem to study pro-groupoids (which are to pro-groups as groupoids are to groups), but I haven't checked if that's really what goes in the last blank. If it does, then they are generalized uniform structures.

   The table is included in most of the pages that it links to, but not the ones for the simplest concepts.