Lax functors are a directed weakening of the notion of functors between (∞,2)-categories.
The goal of this talk is to explain a new model-independent perspective on this concept.
In "A study in derived algebraic geometry" the authors Gaitsgory and Rozenblyum use the
notion of lax functors to define the lax Gray tensor product.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/4234
[3] https://www.mpim-bonn.mpg.de/node/12752