1,387 reputation
11122
bio website poisson.phc.unipi.it/~mossa
location Earth
age 27
visits member for 4 years, 3 months
seen Aug 26 at 10:15
I'm math student, in particular I'm interested in algebra, geometry, topology and category theory (especially higher dimensional category theory) and its application in mathematics.

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