@AaronMazel-Gee hmmm, so can I obtain from this perspective a model structure on say simplicial bialgebras for which simplicial Hopf algebras are fibrant objects?
Does anyone know of a reference for the oo-categorical version of the Eilenberg-Zilber theorem, i.e. that the oo-categorical Dold-Kan correspondence is a symmetric monoidal equivalence?
well, if this is correct it will be rather degenerate -- not unlike a model structure on Monoids where all objects are cofibrant and Groups are exactly the fibrant objects. in this situation, i would say model categories are perhaps a red herring and more relevant is simply the adjunction.
@ManuelRivera (i forgot to tag you)
oops, i missed the word "simplicial"! i guess these can be thought of as corepresentable simplicial presheaves of monoids/groups over affine schemes, and perhaps you can just work in a model category of simplicial presheaves.
@AaronMazel-Gee I am a bit confused: where in the proof do we use that the operad is quadratic? I thought that the argument works as well for n-ary operations...
I read here mathoverflow.net/questions/159735/… that the Eilenberg-Watts theorem in $\infty$-categories has been discussed by some people. Have their conclusions appeared in print? Or perhaps one of you has these WCATSS13 notes David mentions there?
oh, it seems this is in 4.8.4 of Higher Algebra, I hadn't seen it cause "Eilenberg-Watts" is not mentioned. anyway, any other references are still appreciated
Does anyone know a more detailed reference for the very last part of bott's paper "stable homotopy of classical groups" where he does all the root data computations to compute the spaces of minimal geodesics of the relevant symmetric spaces? I'm not so fluent with symmetric spaces and I find his arguments there a bit opaque. I did manage to find down to earth linear algebraic explanation for some of the statements there but I don't think this is possible for all of them...
I'm referring to the last 5 pages of that paper of course...
I mean most likely you can explain everything there by linear algebra. It's just i'm not sure i'm able to come up with these explanations...
@DenisNardin oh sorry, i said that poorly! what i meant was simply: "in order to check that a laxly O-monoidal functor is actually strictly O-monoidal, in general you must check that it strictly respects all n-ary operations, but if O is quadratic then it suffices to check binary operations only." i certainly didn't mean to imply that the proof doesn't work in the general case.
