5,526 reputation
1522
bio website poisson.phc.unipi.it/~mossa
location Earth
age 25
visits member for 2 years, 10 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.


Nov
8
awarded  abstract-algebra
Nov
7
comment Is Aluffi's “Algebra. Chapter 0” a good introduction to algebra?
What's more I don't know of any book of basic algebra that treat representation theory.
Nov
7
answered Isomorphism of quotient ring of polynomial ring
Nov
7
reviewed Approve suggested edit on Isomorphism of quotient ring of polynomial ring
Nov
5
revised Lax algebras as lax morphisms
added 1 characters in body
Oct
31
comment Prove that the elements $2x$ and $x^2$ have no LCM in the ring of integral polynomials with even coefficient of $x$
Right thanks @Doc :)
Oct
31
comment Prove that the elements $2x$ and $x^2$ have no LCM in the ring of integral polynomials with even coefficient of $x$
I'm sorry but $2x^2$ is not the lowest common multiple and is also an element of the ring?
Oct
31
comment Isomorphism theorem
@DanielFischer I thought that the first comment was trying to address the first part of the question: the image of a normal subgroup in a quotient is normal. My mistake.
Oct
31
answered Isomorphism theorem
Oct
31
comment Isomorphism theorem
@Jeh If in the trivial group every subgroup is normal.
Oct
31
comment How to construct a contractible space but not locally path connected?
Actually the space that I'm pretty sure that if you intersect the space above with the closed unitary ball of $\mathbb R^2$ you should find a contractible space non locally path connected which is a cone. The space $X$ should be the intersection of space in the answer with the unit circle.
Oct
31
answered How to construct a contractible space but not locally path connected?
Oct
31
answered Prove that the centralizer subgroup is normal in the normalizer subgroup
Oct
31
comment Is this an accurate portrayal of what category theorists with an interest in the foundations are actually trying to achieve?
Is not opposed, just different. We can deal with foundation in two different ways, the first one I would call applied foundation (like in applied maths) and the second one as theoretical foundation. The first one is interested in codifying all maths concept in the language of a theory and proving the existence of some construction inside the foundational theory. The second is interested in the comparison of different theories which can be used as foundations. The problem is that this second one require a meta-theory i.e. a foundational theory to be developed.
Oct
31
comment Is this an accurate portrayal of what category theorists with an interest in the foundations are actually trying to achieve?
@user18921 The point is that a foundational theory is a theory in which we develop all the mathematics. Once we choose a topos whose theory is our foundational theory all the mathematics we are considering live inside that topos. Comparing different theories (i.e. toposes) is still a large part of logic but that's not foundations.
Oct
29
answered Is this an accurate portrayal of what category theorists with an interest in the foundations are actually trying to achieve?
Oct
29
comment Do adjoint functors really define monads?
@student I've edited the answer. Let me know if now it's more clear.
Oct
29
revised Do adjoint functors really define monads?
improved formatting
Oct
29
comment Do adjoint functors really define monads?
Now I see probably the answer is too long and confusing, I'll try to shorten it a little bit.
Oct
29
comment Do adjoint functors really define monads?
@student Well if you are referring to the last proof then that's just the proof of the exercise in Weibel's book, i.e. that for two generic adjoint functor the equality involving the $\epsilon$ should holds. Instead I'm also convinced that the pair of functor that you have indicated are not adjoint, at least not with the counit you've indicated.