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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

9 votes
Accepted

stackification commutes with finite limits?

The answer is yes, at least for $2$-fiber products. And fortunately there is an excellent reference online: Tag04Y1 in the Stacks Project. I quote: Lemma 8.4. Let $C$ be a site. Let $f : X \to Y$ …
David Roberts's user avatar
  • 35.5k
5 votes

Reference for Manin's idea on algebraic geometry over the symmetric monoidal model category ...

Not really an answer, but as a complement to Myshkin's, let me just mention a predecessor : Deligne's very famous (and magnificent) article Deligne, P. Le groupe fondamental de la droite projective m …
Niels's user avatar
  • 4,008
4 votes

Is there a "free abelian group of rank 1" in the category of affine group schemes?

Claim : if $k$ is perfect of characteristic $0$, then : $$\mathbb Z^{k, alg}\simeq \mathbb G_a\times D_k(k^*)$$ Here $\mathbb Z^{k, alg}$ stands for the pro-algebraic completion of $\mathbb Z$ (the …
Niels's user avatar
  • 4,008
15 votes
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Anabelian geometry study materials?

There is this very beautiful survey Nakamura, Hiroaki; Tamagawa, Akio; Mochizuki, Shinichi The Grothendieck conjecture on the fundamental groups of algebraic curves http://www.math.sci.osaka-u.ac. …
Will Sawin's user avatar
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