12
$\begingroup$

Is there any references on the tensor product of (locally) presentable categories ?

All I know about this is Lurie's book that deals with the $\infty$-categorical version, and a few references that deals with special cases (Grothendieck abelian categories, toposes etc...)

Is there any references that defines it properly and proves the basic properties ?

$\endgroup$
2
  • 2
    $\begingroup$ It's certainly not what you have in mind, but I think it might be worth mentioning that Lurie's work does cover this example too (although I don't think he works out the details in his book): $\mathrm{Set}$ is an idempotent algebra in $\mathrm{Pr}^L$ and modules over it are precisely presentable 1-categories. $\endgroup$ Mar 24, 2019 at 7:08
  • 1
    $\begingroup$ Yes of course ! I know. But as you suspected, I was hopping for more elementary references that could also be read by people only familiar with ordinary category theory. $\endgroup$ Mar 24, 2019 at 7:45

1 Answer 1

15
$\begingroup$

The canonical reference is Chapter 5 of Greg Bird's thesis.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.