QEp 5: From (Model) Categories to Quasicategories

We apply the theorem proven in the previous lecture to two examples:

• We prove the nerve of a category is a quasi-category, by observing that the nerve of a category is in fact the simplicial nerve of a certain Kan enriched category.
• We prove that the simplicial nerve of the full subcategory of fibrant-cofibrant objects of a simplicial model category is a quasi-category.