#so like you might tensor Z[x] over Z with Q to get Q[x] | Explore Tumblr posts and blogs

locally-normal · 6 months ago

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Maybe I should stop telling people I'm an algebraic topologist and just say I do homotopical algebra. It's truer I think. But less well known. Which is weird because everyone knows about homotopy theory.

I guess the brave new algebra program was only fully realized fairly recently.

#probably not enough context here to be understandable #algebra in the sense of mucking about with rings and modules and algebras has been generalized such that #you can just take your module over your nice normal ring and basechange it to be over spheres #so like you might tensor Z[x] over Z with Q to get Q[x]#or you could tensor it over the sphere spectrum with the spheres mod 2 to get something fucked up #Oh I guess I should say derived algebra is what was generalized not regular algebra #but you know.#anyways working over the spheres as your ground ring instead of over the integers is “brave new algebra”#aka homotopical algebra

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