nLab tensor product of stable (infinity,1)-categories

Idea

The tensor product of presentable stable $\infty$-categories (“Lurie tensor product”) is the symmetric monoidal operation which universally co-represents bi-$\infty$-functors that are exact and continuous in each variable (hence which induce triangulated bifunctors on triangulated homotopy categories).

On underlying presentable $\infty$-categories this is just the tensor product of presentable $\infty$-categories.

Related concepts

• triangulated bifunctor

• tensor product of presentable $\infty$-categories

• tensor product of abelian categories

References

• Jacob Lurie; §1.4, §4.8 in: Higher Algebra ($\sim$2017) [pdf]

• Dennis Gaitsgory, Nick Rozenblyum; §6 (pp. 49) in: A study in derived algebraic geometry, Mathematical Surveys and Monographs 221, American Mathematical Society (2017) [ams:SURV/221, book webpage]