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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 12th 2013
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexHow significant is [Enriched ∞-categories via non-symmetric ∞-operads](http://arxiv.org/abs/1312.3178)? >We show that Lurie’s stable ∞-categories from [Lur11a, §1.1] are all enriched in the ∞-category of spectra, and that the R-linear ∞-categories of [Lur11b, §6] are enriched in the ∞-category of R-modules, where R is an E2-ring spectrum. Moreover, we prove that every closed monoidal ∞-category is enriched in itself. This gives us, for example, the natural n-category of functors between any two n-categories, generalizing the familiar fact that the category of categories is enriched over itself.

   How significant is Enriched ∞-categories via non-symmetric ∞-operads?

   We show that Lurie’s stable ∞-categories from [Lur11a, §1.1] are all enriched in the ∞-category of spectra, and that the R-linear ∞-categories of [Lur11b, §6] are enriched in the ∞-category of R-modules, where R is an E2-ring spectrum. Moreover, we prove that every closed monoidal ∞-category is enriched in itself. This gives us, for example, the natural n-category of functors between any two n-categories, generalizing the familiar fact that the category of categories is enriched over itself.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 18th 2013
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   Author: Urs
   Format: MarkdownItexAh, it's finally out. Thanks for the pointer, I had almost missed it. Added this to _[[enriched (infinity,1)-category]]_ now. This is as significant as ordinary enriched category theory plus $\infty$-category theory together. Will be foundational stuff in the future that begins now.

   Ah, it’s finally out. Thanks for the pointer, I had almost missed it. Added this to enriched (infinity,1)-category now.

   This is as significant as ordinary enriched category theory plus $\infty$-category theory together. Will be foundational stuff in the future that begins now.