1,237 reputation
1721
bio website poisson.phc.unipi.it/~mossa
location Earth
age 26
visits member for 3 years, 2 months
seen 12 hours ago
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
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
Dec
31
comment Is there a precise definition of “mathematical formula”?
I suppose, I actually never studied this stuff by any particular book but used course notes. I believe that all these basic definition can be easily find in course notes of a course in mathematical logic.
Dec
31
answered Is there a precise definition of “mathematical formula”?
Nov
13
awarded  Self-Learner
Oct
10
comment Completeness theorem via syntactic categories
@OmarAntolín-Camarena that's actually the answer to the question: quoting directly from the nlab " By the Yoneda lemma, the syntactic category $Syn(T)=C_T$ contains a “generic” model of the theory. Moreover, by the construction of $C_T$ (see syntactic category), the valid sequents in this model are precisely those provable from the theory."
Oct
1
awarded  Caucus
Sep
30
awarded  Nice Question
Jul
20
awarded  Popular Question
Jun
24
accepted Further relation between monads and theories
Jun
20
asked Further relation between monads and theories