6,526 reputation
1727
bio website poisson.phc.unipi.it/~mossa
location Earth
age 26
visits member for 3 years, 7 months
seen 2 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.


May
3
answered Natural transformation is a mono iff the components are.
Apr
29
comment Does Gödel's Completeness Theorem still hold even if the set of variables is finite?
@MauroALLEGRANZA I agree that probably Manin assume the hypothesis of infinite set of variables. Nonetheless my observation is that the proof of completeness theorem doesn't seems requiring the infinity of the set of variables in order to be proven.
Apr
28
comment Does Gödel's Completeness Theorem still hold even if the set of variables is finite?
@Amr Following your argument: if you have to prove an $L$-formula somewhere in your proof you are gonna eliminate the $10$-th variable by an application of a generalization and a particularization (application of modus ponens to formulas of the form $\forall x A(x) \rightarrow A(t)$ for $t$ a term). My conjecture is that by replacing in your proof every occurence of the variable with the term is used in the particolarization you should still be able to have a valid proof. Anyway I could be wrong, that's why I said that I suppose that should work :)
Apr
28
answered Does Gödel's Completeness Theorem still hold even if the set of variables is finite?
Apr
17
awarded  Nice Answer
Apr
11
comment Query on a simple exercise involving representations of functors.
@Niels.Remb05 take a look to the edit and see if that solves all your doubts.
Apr
11
revised Query on a simple exercise involving representations of functors.
Added specifications
Apr
11
comment Query on a simple exercise involving representations of functors.
It follows by the definition of the yoneda isomorphism. In some minutes I'm gonna add that to the answer. :)
Apr
11
answered Query on a simple exercise involving representations of functors.
Apr
10
revised When is $\langle x,y\rangle$ equal to $\langle x\rangle\langle xy\rangle$?
edited title
Apr
9
answered Preservation of Limit by Hom: Naturality Question.
Apr
8
comment Do we lose everything, if the natural transformations in a monad are exactly inverse?
@NiftyKitty95 $\eta_{TA} \circ \mu_A$ while being well typed is usually false for monads. Consider $T$ the free monoid monad then for every set $X$ we have $T(X)$ the free-monoid. Now $\mu_X((x),(y))=(x,y)$ where $x,y \in X$ and $\eta_{TX}\circ \mu_X ((x),(y))=((x,y)) \ne ((x),(y))$ to $\eta_{TX} \circ \mu_X \ne 1_{TTX}$.
Mar
31
answered Showing hom-sets are disjoint in a morphism category
Mar
31
comment Spec($A$) is connected if $A$ is local
@WLOG Right I supposed that it was well known notation: $D(I) = Spec(R) \setminus V(I)$ a standard open set.
Mar
31
answered Spec($A$) is connected if $A$ is local
Mar
31
revised Spec($A$) is connected if $A$ is local
Corrected a typo.
Mar
24
comment What is category theory?
@AsafKaragila I would glad to hear your opinion about it :) (maybe in a chat?)
Mar
24
comment What is category theory?
@Number9 "is category theory widely accepted?" the answer is "it depends, what do you mean for category theory being accepted?"
Mar
24
comment What is category theory?
@Number9 You need collections like the class of all set, of all groups and so on. If you just stop to classes you could add just those axioms that ensure the existance of such families. Of course Grothendieck axioms give all that, but it also allows to use bigger collections.
Mar
24
answered What is category theory?