thel
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Besides Gaitsgory-Rozenblyum (http://www.math.harvard.edu/~gaitsgde/GL/), you might try looking at Lee Cohn's work (http://arxiv.org/abs/1308.2587), which establishes some equivalence between the ...

Deligne's article, 'Categories Tannakiennes,' section 5 would be a good place to look. It was published in the Grothendieck Festschrift, vol. 2.

The existence of such an adjunction implies that $B \otimes -$ preserves limits, which doesn't seem very likely. Here is a counterexample, though probably not the simplest one. Set $B = k[y]$ and ...

You can get a pretty good birds-eye view by reading this 2004 Oberwolfach report (no. 17): http://www.mfo.de/document/0414/OWR_2004_17.pdf Calculus of Functors is the theme of the 2012 Talbot ...

This Fourier transform is positive, supported everywhere, and has polynomial decay. It is the Poisson kernel evaluated at time 1, up to some rescaling. http://en.wikipedia.org/wiki/Poisson_kernel

I don't think this is actually an injection on isomorphism classes. We can see this by restricting to extremely nice spaces, say finite simply-connected CW complexes with free homology. In this ...

Let $\zeta_k$ be a countable dense sequence of points in the boundary and consider $f(z) = \sum \frac{1}{2^k} \frac{1}{z-\zeta_k}$. The sum is plainly uniformly convergent on any subset of finite ...

For finite spectra, your question is precisely Freyd's generating hypothesis, which is open.

Fix an integer $n$. The dimension of a vector space $V$ is divisible by $n$ iff $V$ can be given the structure of a representation of the discrete Heisenberg group $H_n$ with central charge $1$. This ...

No. Consider the case where your sets happen to be abelian groups with an action of G. Pushing out the zero morphism over any map gives the cokernel, so a special case of your question is whether ...

Look at Bredon's 'Sheaf Theory', Chapter Six: "Cosheaves and Cech Homology" I am not aware of any quasi-coherent story.