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Dec 10, 2010 at 1:31 comment added David Roberts To quote from Clark Barwick's arXiv paper math/1012.1889 out today, "We use the Universe Axiom of [SGA4 I, Exp I, §0], and we fix two universes U ∈ V. All rings, modules, schemes, etc., will be U-small. We employ the following notational conventions for categories or ∞-categories: (N.1) Roman characters A, B, C, . . . , etc., will denote categories and ∞-categories that are essentially V-small and locally U-small. (N.2) Bold characters A, B, C, . . . , etc., will denote categories and ∞-categories that are locally V-small."
Dec 9, 2010 at 22:26 history edited David Roberts CC BY-SA 2.5
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Dec 9, 2010 at 21:46 comment added BCnrd Kevin, whenever we form Ext-sheaves, those Hom's had better be sets or else it is really confusing what is going on.
Dec 9, 2010 at 20:59 history edited David Roberts CC BY-SA 2.5
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Dec 9, 2010 at 20:53 comment added Kevin Buzzard This is great---thanks. I think this answer more than justifies the existence of the question.
Dec 9, 2010 at 20:40 history answered David Roberts CC BY-SA 2.5