7
votes
2answers
359 views
Is the tensorproduct of a triangulated category with a ring again triangulated?
$\underline{Background}$ :
Suppose $\tau$ is a preadditive category and $R$ a ring. Then one may form a new preadditive category $\tau \otimes R$ in the following way:
$\tau \ot …
0
votes
0answers
160 views
Maxwell’s equations in developed form [closed]
Can someone write in a developed form a macro Maxwell's equations from wikipedia link. I have problem because I am not sure what is a scalar and what is a vector?
http://en.wikipe …
8
votes
3answers
595 views
Why is a monoid with closed symmetric monoidal module category commutative?
Given a symmetric monoidal category and a monoid object A in it, one can form the category of modules over this monoid object, i.e. objects are $A \otimes M \rightarrow M$ satisfyi …
1
vote
2answers
150 views
Condition for Uniqueness of Measures
Let be $\Omega$ a compact metric space, $\mathcal{B}(\Omega)$ the $\sigma$-algebra of Borelian sets of $\Omega$ and
$\mathcal{M}_1(\Omega)$ the set of all probabilities defined on …
0
votes
0answers
328 views
merging two channels [closed]
Given two channels ${A_1,B_1,P_1}$ and ${A_2, B_2, P_2}$ with capacities $c_1, c_2$ respectively, where $A_1,A_2$ are disjoint sets of input symbols, $B_1,B_2$ disjoint sets of out …
6
votes
4answers
2k views
Regular languages and the pumping lemma
In certain dark corners of computer science and group theory, one often wants to prove that a language is not a regular language (ie a language accepted by a finite state automaton …
4
votes
2answers
384 views
Conjugate cocharacters in a maximal torus
Let $G$ be a linear algebraic group over an algebraically closed field $k$, and $T$ a maximal torus of $G$.
Suppose we have two cocharacter $\mu, \mu' : \mathbb{G}_m \to T$, which …
1
vote
0answers
104 views
limit and colimit for L_\infty algebras
Hi, how can one take (homotopy) limit and colimit of L_\infty algebras? Are there some explicit formulas? For example, here the most relevant is to take push-out of a diagram in L_ …
4
votes
2answers
1k views
If you went into a coma now and woke in twenty years time what would be your first post on MO? [closed]
This is just for fun. You can assume you retain full use of your faculties. I don't have anything to add to the question, although that may change depending on the responses. The t …
7
votes
3answers
550 views
An Operation on Multisets
Define a 2 x n array of positive integers where the first row consists
of some distinct positive integers arranged in increasing order, and the second row consists of any positive …
15
votes
3answers
506 views
Do decidable properties of finitely presented groups depend only on the profinitization?
This is a just-for-fun question inspired by this one. Let $P$ be a property of finitely presentable groups. Suppose that
The truth of $P(G)$ only depends on the isomorphism class …
10
votes
1answer
481 views
Potential semi-stability of etale cohomology of etale covers.
Let $\mathbf{Q}_p$ denote the field of $p$-adic numbers.
Suppose that $K/\mathbf{Q}_p$ is a finite extension, and let $O_K$ denote the ring of integers of $K$. Suppose that $X$ is …
2
votes
1answer
282 views
Describe the second cohomology group $H^2(Z_n \times Z_n. k^*)$.
I would like to write down explicitly the generating cocycles of this second cohomology group, $H^2(Z_n \times Z_n, k^*)$. Here $k$ is an algebraically closed field of characteris …
2
votes
1answer
562 views
Hyperbolic structure on surfaces with boundary
I have following two questions
1) Let $S$ be a compact oriented surface with (non-empty) boundary. Also assume that the Euler characteristic of $S$ is negative (Thus, $S$ is not d …
9
votes
1answer
410 views
Descent of closed subschemes over finite fields
Let $p$ be a prime number, and $k$ a finite field with $q=p^n$ elements. Let $X$ be a scheme over $k$ and denote by $X'$ its base change to an algebraic closure $\bar k$ of $k$. De …
