6,431 reputation
1626
bio website poisson.phc.unipi.it/~mossa
location Earth
age 26
visits member for 3 years, 6 months
seen 5 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
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
Jul
14
answered Action of factor group on a group
Jul
12
answered Adjoint functors requiring a natural bijection
Jul
8
comment Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
@RoyO. I'm probably a little rusty, but isn't it true that a reduction of a term has complexity less than the starting term?
Jul
8
answered Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
Jul
6
reviewed Approve Torsion free flat module over a discrete valuation ring is Cohen-Macaulay
Jul
4
revised On the category of Sets as an example of an algebraic category
Improved answer
Jul
4
comment On the category of Sets as an example of an algebraic category
@DanaeKissinger Ok, then I think my answer said something about that too, let me edit a little bit to make it clear.
Jul
4
answered On the category of Sets as an example of an algebraic category
Jul
2
awarded  Curious
Jun
25
answered Variables in Types in type theory
Jun
20
comment How do definitions work in Martin-Lof type theory?
Anyway if you have more question I suppose it's better to go in chat :)
Jun
20
comment How do definitions work in Martin-Lof type theory?
Definitions are the rules for the type.
Jun
20
comment How do definitions work in Martin-Lof type theory?
@user18921 Definition of inductive type in a type theory works like the definition of any other type: you state a rule for the introduction of the type (one that state that the constant of language that represent the type is indeed a type) and some constructors, eliminators and computational rules. The only difference is that such rules are required to have a certain format.
Jun
19
answered How do definitions work in Martin-Lof type theory?
Jun
12
comment Types, Sets and Categories
@CristianGarcia $C_0$ is the type, so of course they have all the same type :), at least this is the usual type theoretic definition of category.
Jun
12
answered Typed Category Theory?
Jun
12
comment Using types instead for basic proofs
@ChristianGarcia Are you trying to consider membership as a relations in the proposition as type paradigm?