Giorgio Mossa
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 Mar 15 awarded Popular Question Feb 20 awarded Enlightened Feb 20 awarded Nice Answer Jul 30 comment Does every Lawvere theory arise in this way? @goblin is perfect. Jul 28 comment Does every Lawvere theory arise in this way? Can you give a more detail on what $Lawv(X)$ should be? It should be the smallest finite product sub-category of $\mathbf C$ containing $X$? It should be the smallest finite product category generated by $X$ and its algebraic morphism? May 9 awarded Yearling Apr 29 awarded Good Answer Feb 20 answered The groupoid of algebraic expressions and proofs Feb 17 awarded Favorite Question Dec 5 answered Relations between ordinary functor categories and higher categories Dec 2 awarded Critic Nov 9 awarded Necromancer Jul 2 answered Basic category theory: Universality of adjunction unit is justified by Yoneda Proposition in Mac Lane's text Jul 2 comment Basic category theory: Universality of adjunction unit is justified by Yoneda Proposition in Mac Lane's text I don't understand, what you mean by "of course, this is not explicitly defined in general, since it depends on the particular adjunction"? Jul 2 awarded Curious May 21 comment Simple show cases for the Yoneda lemma @HansStricker what do you mean by $K_1$ and $K_2$ are the representable functors? May 21 comment A categorical characterization of ordinal numbers I guess that for help could be useful to characterize $\star$ by universal property, otherwise is not clear what a category (not necessarily a subcategory of $\mathbf{Cat}$) closed by $\star$ should be. May 20 comment A categorical characterization of ordinal numbers Note that in the note you have linked Joyal define $\star B$ as a functor of type $\mathbf {Cat} \to B\setminus \mathbf {Cat}$ not $\mathbf {Cat} \to \mathbf {Cat}$. May 20 comment A categorical characterization of ordinal numbers The operation $\star$ does not commute with colimit: indeed if that where true then for every limit ordinal $\lambda=\bigcup_{\gamma < \lambda} \gamma$ you should have that $\lambda+1=\lambda\star[0]=\bigcup_{\gamma < \lambda} \gamma\star[0]=\bigcup_{\gamma < \lambda}\gamma+1=\lambda$ things that's not possible since $\lambda$ doesn't have a max while $\lambda+1$ does. May 9 revised Further relation between monads and theories fixed grammar