Timeline for What is the definition of a $\mathcal{U}$-category?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 26, 2021 at 10:29 | vote | accept | Jxt921 | ||
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Nov 2, 2018 at 17:59 | comment | added | Mike Shulman | I'm not really convinced by your #2, because I think very rarely in category theory does one want to talk about a "set of objects" of some large category anyway. What we actually talk about all the time are set-indexed families of objects, and those should work equally well regardless of what choice is made here. The only case I can think of where we talk about a "set of objects" is when the set is a generating set, but even in such cases it is always just as good to talk about an indexed family. | |
| Nov 2, 2018 at 10:38 | comment | added | Jxt921 | But isn't the approach where one requires a set of objects to belong to the successor universe is essentially the same where one requires nothing about it? Indeed, let $\mathsf{C}$ be a category where for any $X,Y \in \mathsf{C}$ we know that $\mathsf{Hom_C}(X,Y) \in \mathcal{U}$? Then by the axiom of universes we have a universe $\mathcal{V}$ which contains the set $\{\mathsf{Ob(C)}, \mathcal{U} \}$, that is, which contains $\mathsf{Ob(C)}$ and which is a successor of $\mathcal{U}$. | |
| Nov 1, 2018 at 20:44 | history | answered | Reid Barton | CC BY-SA 4.0 |