Factorizations and filtrations in $(\infty,\infty)$-category theory

Recently, the theory of $(\infty,\infty)$-categories has undergone significant development, in part because of applications to mathematical physics and geometric topology. In order to work with these structures, it is useful to try to generalize some of the methods of algebraic topology to this setting. In this talk, we will recall the basic definitions and discuss how certain techniques from homotopy theory can be carried over into the higher categorical world.