The Homotopical Canonical Grothendieck Topology

Every category can be equipped with the canonical Grothendieck topology, which can be explicitly described using colimits. However, colimits are not homotopy invariant. By instead using homotopy colimits we can define a homotopy invariant canonical Grothendieck topology on any simplicial model category. I will explain the homotopical version of the canonical Grothdendieck topology, showcase some examples and discuss some open questions.