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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
May
9
awarded  Yearling
Feb
1
awarded  Popular Question
Jan
29
answered comparison between two monadic definitions for an operad