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 definitions 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 nlab noncommutative noncommutative-geometry number-theory object 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

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 30th 2018
   • (edited Jun 30th 2018)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIn John Huerta's [quest](https://golem.ph.utexas.edu/category/2018/06/elmendorfs_theorem.html) to understand Elmendorf's theorem, Mike has pointed him towards inverse EI (∞,1)-categories. Our coverage of [[EI-categories]] and related things is poor as yet. We could do with the $(\infty,1)$-version and then 'inverse' such. Clark Barwick [suggested](https://nforum.ncatlab.org/discussion/7301/parametrized-higher-category-theory-and-higher-algebra/?Focus=65113#Comment_65113) that >’EI ∞-categories’ essentially are stratified spaces. Is there enough of a difference to warrant two or three pages to discuss EI-/EI $(\infty,1)$-/inverse EI $(\infty,1)$-categories, or can we do it on one page?

   In John Huerta’s quest to understand Elmendorf’s theorem, Mike has pointed him towards inverse EI (∞,1)-categories. Our coverage of EI-categories and related things is poor as yet. We could do with the $(\infty,1)$-version and then ’inverse’ such.

   Clark Barwick suggested that

   ’EI ∞-categories’ essentially are stratified spaces.

   Is there enough of a difference to warrant two or three pages to discuss EI-/EI $(\infty,1)$-/inverse EI $(\infty,1)$-categories, or can we do it on one page?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJun 30th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI think "inverse EI" warrants a separate page from merely EI. But for the present I think it would be sufficient to redirect EI $(\infty,1)$-categories to EI 1-categories, until someone has something contentful to add that's specifically about one or the other.

   I think “inverse EI” warrants a separate page from merely EI. But for the present I think it would be sufficient to redirect EI $(\infty,1)$-categories to EI 1-categories, until someone has something contentful to add that’s specifically about one or the other.