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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.