I have a question concerning the Grothendieck's universe:
Let fix a GUniverse $U$. Is a $U$-set the same as a $U$-category or is there a subtle difference?
2026-02-22 21:48:30.1771796910
Grothendieck Universe
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The term "$\mathcal{U}$-set" doesn't exist. There are terms "$\mathcal{U}$-small set", "$\mathcal{U}$-small category", "$\mathcal{U}$-category". Definitions of them may differ, but all variants are more or less the same as in SGA. Such definitions are listed in one of my previous answers.