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40m
comment reference for groupoid cohomology
This is essentially just fancy language for the statement that the cohomology of a discrete group $G$ can be computed as the cohomology of the space $K(G,1)$.
4h
comment Can the projective line be provided with a ring structure?
@WolfgangTintemann: Yes, it is obtained by conjugating addition on $\mathbb{R}/\pi\mathbb{Z}$ by the homeomorphism $\tan:\mathbb{R}/\pi\mathbb{Z}\to\mathbb{P}^1_{\mathbb{R}}$.
19h
revised When did people know that all real polynomials of degree greater than 2 are reducible?
edited tags
1d
comment Reference for (co)limit-preserving functor $X\mapsto R^X$
I wonder what can be said in general about (say, presentable) categories $\mathcal{C}$ such that the functor $\text{set}^{op}\to\mathcal{C}$ sending $X$ to the power $I^X$ preserves finite colimits, where $I$ is the initial object. Everything I said here applies to any such category; in particular, the functor $\mathcal{C}\to\text{Set}$ corepresented by the object $I^2$ can be lifted to a right adjoint $G:\mathcal{C}\to\text{Bool}$ that in some sense provides $\mathcal{C}$ with robust notion of "idempotents".
1d
revised Reference for (co)limit-preserving functor $X\mapsto R^X$
added 710 characters in body
1d
answered Reference for (co)limit-preserving functor $X\mapsto R^X$
Jul
30
answered Adjointable Abelian Monoidal Functor
Jul
29
reviewed No Action Needed What am I missing in this highly oscillatory integral?
Jul
26
comment Is there a generalization of homotopy groups to fractional dimensions
If there were a "$1/2$-sphere" $S^{1/2}$, you would probably expect it to be a pointed space for which $S^{1/2}\wedge S^{1/2}$ is weak equivalent to $S^1$. It is easy to show (using homology, for instance) that no such space exists. This doesn't prove there is no sensible notion of $\pi_{1/2}$, but it is some evidence against it.
Jul
26
comment Bohr compactification and “discretization”
Yes, that's right.
Jul
26
comment On the global structure of the Gromov-Hausdorff metric space
For any $r>0$, there is an autohomeomorphism of $\mathcal{GH}$ that takes a compact metric space and scales its metric by $r$.
Jul
25
answered Bohr compactification and “discretization”
Jul
24
comment Which combinations of normality, separability, and paracompactness do complex manifolds possess?
How do you define holomorphic charts on your example?
Jul
24
comment Which combinations of normality, separability, and paracompactness do complex manifolds possess?
A complex manifold must have a set of charts with holomorphic transition functions, not just be locally homeomorphic to $\mathbb{C}$.
Jul
24
accepted Löwenheim-Skolem for many-sorted theories
Jul
23
reviewed Approve Löwenheim-Skolem for many-sorted theories
Jul
23
awarded  Good Answer
Jul
23
revised Löwenheim-Skolem for many-sorted theories
deleted 326 characters in body
Jul
23
comment Löwenheim-Skolem for many-sorted theories
@Goldstern: Ah, very nice! So the problem is definitely more complicated than I thought. Let me edit the question a bit to reflect this.
Jul
23
comment (A kind of) Irreducibiliy of regular open convex sets in the Cartesian space
Given any point $y$ in $V$, if you draw a line segment from $y$ to $x$, and then extend the line segment a little bit past $x$, you will enter the set $W\cdot U$. Thus $x$ lies on the line segment joining $y$ to some point in $W\cdot U$. Since $W\cdot U\leq C$ and $C$ is convex, $y\in C$ would imply $x\in C$.