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May
14
comment Do Boolean rings always have a unit element?
My definition of ring includes a $1$, and my definition of boolean algebra also includes a $1$.
May
14
answered Commuting square of functors
May
12
comment Why does every countable limit ordinal have cofinality $\omega$?
If there is a cofinal $\alpha$-sequence in $\beta$ and a cofinal $\beta$-sequence in $\gamma$, then there is a cofinal $\alpha$-sequence in $\gamma$. Therefore cofinalities are initial ordinals.
May
12
answered Viewing groups as objects of the concrete category $\mathsf{Grp}$
May
11
answered Commutativity of a sheaf of groups from an epimorphism
May
11
answered Space modelled on ring
May
11
comment Space modelled on ring
Functors are not the best way to think about schemes if you're looking for spaces modelled on rings. Rather, a scheme is a locally ringed space that is locally isomorphic to the spectrum of a ring. There is a functorial way of looking at schemes but I find it much more artificial.
May
11
comment Space modelled on ring
Do you mean a scheme?
May
10
comment A question about partitioning the unit cube into simplexes
There is a triangulation of the $n$-cube satisfying condition (1): it is what is obtained by considering the simplicial set $(\Delta^1)^n$. I haven't thought about (2).
May
9
comment Axiom of Choice-esque argument to show that a proof of a statement exists without actually giving a proof
Any such category or topological space must be connected: everything proves $\top$, and $\bot$ proves everything.
May
9
comment Is $\mathbb{N}$ impossible to pin down?
If you believe that there is a "real" $\mathbb{N}$, then it sounds like you've pinned it down already!
May
8
comment $C(X) \cup C(Y) = C(X \cup Y)$ if $C$ is an algebraic closure and $X, Y$ are finite?
The smallest closed subset containing $C(X)$ and $C(Y)$ is $C(X \cup Y)$. But in general that is not $C(X) \cup C(Y)$.
May
7
answered Existence of not locally small categories
May
7
comment Is a divisor in the hyperplane class necessarily a hyperplane divisor?
Hmmm... yes, I suppose that is true. Do you have a better proof for the plane curve case, then?
May
7
comment Is a divisor in the hyperplane class necessarily a hyperplane divisor?
Well, if if $h$ is a rational function, then there are some coprime $F$ and $G$ such that $h = F / G$. If they weren't of degree $1$ then that would contradict the condition on the degrees of the divisors.
May
7
comment Is a divisor in the hyperplane class necessarily a hyperplane divisor?
If $F$ and $G$ are homogeneous of degree $m$ and coprime, then $F / G$ will be a rational function with $m \deg H$ zeros and $m \deg H$ poles, counted with multiplicity, by Bézout's theorem.
May
7
comment Can “proving mathematical theorems” as a 1 player puzzle be studied in combinatorial game theory?
See Wikipedia about game semantics.
May
7
comment Can “proving mathematical theorems” as a 1 player puzzle be studied in combinatorial game theory?
Actually, it's a two-player game between the verifier and the refuter.
May
6
asked Is a divisor in the hyperplane class necessarily a hyperplane divisor?
May
6
comment Existence of not locally small categories
If those authors don't admit the existence of locally small categories, why would they talk about such things? To talk about such things would require them to admit there are categories that are not locally small! But one sometimes speaks of ‘metacategories’.