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  • Locally small categories - Mathematics Stack Exchange
    The category of locally small categories, what we usually mean by $\mathbf{Cat}$ is not locally small This is easy to show: consider the endofunctors of $\mathbf{Set}$, i e $\mathbf{Cat}(\mathbf{Set},\mathbf{Set})$ Just considering constant functors already produces a proper class as there's a constant functor for each set
  • Locally Closed Immersion - Mathematics Stack Exchange
    The goal is to show that the diagonal morphism $\Delta_X: X \to X \times_S X$ is a locally closed immersion
  • abstract algebra - Locally Noetherian schemes are quasiseparated . . .
    $\begingroup$ It is better if you know that every affine open of a locally Noetherian scheme is the spectrum of a Noetherian ring That way you are not stuck with just the given covering $\mathrm{Spec}(A_i)$ $\endgroup$
  • the equivalency of two definitions of locally closed sets
    Tour Start here for a quick overview of the site
  • What are presentable categories? - Mathematics Stack Exchange
    I will speak about $\mathbf{Cat}$ as an ordinary locally small category There is no significant difference between the the various notions because filtered colimits in $\mathbf{Cat}$ preserve equivalences, and so a category is finitely presentable in the bicategorical sense if and only if it is equivalent to one that is finitely presentable in the enriched sense, and because the 2-categorical
  • The product of locally compact spaces is locally compact
    What I was trying to say is that people usually assume things are Hausdorff, just to sometimes make their life easier When they do this, they say "locally compact Hausdorff" But if someone said "locally compact and Hausdorff", I would think they were emphasizing the word "Hausdorff", which would be weird
  • algebraic geometry - Constant sheaf vs locally constant sheaf . . .
    $\textbf{Locally constant sheaf}$: A sheaf $\mathcal{F}$ such that there is an open cover ${U_{\alpha}}$ of X with $\mathcal{F}|_{U_{\alpha}}$ is a constant sheaf I know that a constant sheaf is a locally constant sheaf but I don't see why a locally constant sheaf isn't a constant sheaf





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