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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 6th 2011

added to filtered (infinity,1)-category the statement that these are precisely those shapes of diagrams such that $\infty$-colimits over them commute with finite $\infty$-limits.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeJan 14th 2011

By the way, it seems in Joyal’s lecture notes from Barcelona he says directed when we would say cofiltered; usually directed is just a special case, but he means in general (the same remark both for 1-categorical and the quasi-categorical context).

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