In this active learning session we first discussed the following question by the students:

• Why the functors C and N are in fact adjoint functors between simplicial sets and simplicially enriched categories. 
• We sketched why the functor C preserves inclusions, by recalling the fact that pushout preserves inclusions of sets. 
• We also gave a detailed computation of C of the boundary of Delta[2].
• We also tried to answer whether the underlying category of C[S] depends only on S_0 and S_1.

Then we discussed following additional topics:

• We can use the adjunction (C,N) to think about quasi-categories as ``weak" Kan-enriched category.
• For a given simplicial model category M, there are three ways to construct homotopy categories: as a simplicial category, as a model category and as a quasi-category and they all coincide.
• How to construct a quasi-category out of a topological monoid.