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James Deikun (Oct 25 2024 at 13:43):I'm looking for any references that explore or use the tensor product of locally presentable categories. I tried following citation trails from the thesis of Gregory Bird, but I didn't find anything that looked likely in the direct citations, and the two main books on the subject have endless citations so it seemed hopeless to look in there without any direction.
Chaitanya Leena Subramaniam (Oct 25 2024 at 16:55):For an explicit definition see Reid Barton's thesis (specifically, Section 4.8). The ultimate reference is Chapter 4 (specifically Section 4.8) of Lurie's Higher Algebra, but is harder to read.
James Deikun (Oct 25 2024 at 23:29):Thanks for these, the explicit construction in Barton and the viewpoint in terms of multivariable adjunctions are very helpful!