8:06 AM
@JonathanBeardsley I was an undergrad just two years ago. Personally I (and a number of friends ) really enjoyed Emily's: https://math.jhu.edu/~eriehl/context.pdf
But now I find it useful to see it in action: say the first few chapters of Weibel's Homological algebra/Moerdijk McLane's Sheaves in Geometry and Logic.

8:56 AM
I haven't really read either, but Tom Leinster's book also looks nice and a bit more basic than Emily's: arxiv.org/abs/1612.09375

15 hours later…
11:57 PM
Hi everyone, I hope this isn't too basic a question, but I'm looking for a citation or quick proof that localization of a simplicial $k$-algebra is flat.

If $R$ is a simplicial $k$-algebra, my definition of localization at an $f \in \pi_0 R$ is $R otimes_{k[x]}^L k[x]_f$ where $R$ is a $k[x]$-algebra via $x \mapsto f$. My definition of a flat map $A \to B$ is that $\pi_0 B$ is flat over $\pi_0 A$ and $\pi_i A \otimes_{\pi_0 A} \pi_0 B \to \pi_i B$ is an isomorphism. Let me know if these definitions are wrong too!