6,356 reputation
1625
bio website poisson.phc.unipi.it/~mossa
location Earth
age 26
visits member for 3 years, 5 months
seen 11 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.


1d
revised System of generators and surjective homomorphism
added 75 characters in body
1d
comment System of generators and surjective homomorphism
@MartinBrandenburg ops... thanks for pointing out, I'm going to edit immediately.
1d
answered System of generators and surjective homomorphism
2d
revised Homotopy Groups for Categories
deleted 4 characters in body
2d
answered Homotopy Groups for Categories
2d
comment Homotopy Groups for Categories
I wouldn't dare to call this constuction $\pi_1$ of a category, mainly because this is structure distinguish an n-tuple of composable arrows in the category and their composite....
Nov
21
comment Why is this not a category?
A little add: if instead one consider the families $mor_{\mathbb P}(O,Q)$ of decreasing monotone functions these data do not form a category.... well not in the natural way.
Nov
21
answered Why is this not a category?
Sep
30
awarded  Explainer
Sep
23
awarded  Revival
Sep
8
accepted Category of pointed manifolds
Sep
8
asked Category of pointed manifolds
Jul
17
revised Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
made some correction
Jul
17
comment Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
@RoyO. After a deep reading of the book you cited above I think I've finally found a solution to your problem, take a look and let me know if it's not clear :)
Jul
17
revised Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
Corrected the answer
Jul
16
comment Algebras of the environment monad
@MartinBrandenburg aaaaaah I see now. I'm sorry I've misread the question, anyway since it seems that the OP seems interested I think it would better leave it....
Jul
16
revised Algebras of the environment monad
added 2 characters in body
Jul
16
comment Algebras of the environment monad
@JeffRussell yes, because $(-)^E \circ (-)^E={(-)^E}^E$ so by the isomorphism ${(-)^E}^E \cong (-)^{E \times E}$ (a.k.a. the exponential law) we get the monad structure.
Jul
15
comment Algebras of the environment monad
@MartinBrandenburg The OP asked "Is there a more natural way to describe these things?" I presented such monad as the image of the comonoid through the yoneda embedding, isn't it a different way to describe the monad?
Jul
15
answered Algebras of the environment monad