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1. • CommentRowNumber1.
   • CommentAuthorJon Beardsley
   • CommentTimeOct 16th 2012
   • (edited Oct 16th 2012)
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   Author: Jon Beardsley
   Format: MarkdownItexDoes anyone know if there is a characterization of subcategories of a stable symmetric monoidal $\infty$-categories which give you thick subcategories in the homotopy category? Localizing subcategories?

   Does anyone know if there is a characterization of subcategories of a stable symmetric monoidal $\infty$-categories which give you thick subcategories in the homotopy category? Localizing subcategories?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeOct 17th 2012
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   Author: Mike Shulman
   Format: MarkdownItexCan you say anything about what would you expect to be different about such a characterization from the triangulated-category one? (I mean, since a stable $(\infty,1)$-category determines its homotopy category, any property of the homotopy category is also a property of the $(\infty,1)$-category.)

   Can you say anything about what would you expect to be different about such a characterization from the triangulated-category one? (I mean, since a stable $(\infty,1)$-category determines its homotopy category, any property of the homotopy category is also a property of the $(\infty,1)$-category.)