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When Lurie says phrases like “preserves filtered colimits” or “admits filtered colimits”, should I always assume he omitted the word “small” if he doesn’t explicitly emphasize not to?
I’d been subconsciously inserting it previously, but I’ve been trying to pay attention to finer details lately and noticed switching in places that seemed odd (e.g. definition 5.3.4.5 of continuous functor and compact object) and inconsistent (e.g. proposition 5.3.4.10). So I’m wondering if my previous habit was correct – that I should always be inserting “small” – or if there are times when Lurie really does intend to distinguish between the two classes in places without emphasizing it.
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