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I had started to expand Eilenberg-Watts theorem a little. Stated it in more modern form as an equivalence of categories. Also started adding pointers to Hoyes homotopy-theoretical versions, but then I ran out of steam for the moment. I should come back to this later.
Is there more than Hovey’s article on the higher-algebra/homotopy-theoretic versions?
I see that the first half of Eilenberg-Watts in $\infty$-category theory is in Higher Algebra cor. 4.3.5.15 (now recorded in the entry here).
I wouldn’t be surprised if the second half/converse statement is also hidden there somewhere, but so far I don’t see it…
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