bio | website | poisson.phc.unipi.it/~mossa |
---|---|---|
location | Earth | |
age | 26 | |
visits | member for | 3 years, 2 months |
seen | 12 hours ago | |
stats | profile views | 1,200 |
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 |