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I am feeling a bit silly about the following, as this is probably easy and I must be being dense, but I’ll throw this out as a question now anyway:
given an ∞-functor f:X⟶Y between ∞-groupoids, we get an induced pullback
f*:EMod(Y)⟶EMod(X)for E any E∞-ring and EMod(−)≔Func(−,EMod) the ∞-category of E-∞-modules on X.
This f* should be closed monoidal, I suppose. I can see a pseudo-proof, but I am a bit stuck with making it a rigorous proof. Can anyone help?
Ah, I realize that I am looking here exactly for the ∞-version of Mike’s article
The context is example 2.2 there, with V now the ∞-category EMod, and I am after the ∞-analog of the consequence example 2.17 of theorem 2.14 there.
With a minimum of enriched ∞-category theory all this should just go through verbatim…
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