Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.
Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
Covers the construction of a left adjoint to the singular set functor, comparing the homotopy theory of topological spaces with that of simplicial sets.
Covers the combinatorics of the simplex category and its equivalence to topological spaces, as well as the concept of functor categories for cosimplicial and simplicial objects.
Explores higher-order interactions in brain networks using simplicial complexes and information theory, analyzing data from fMRI, financial time-series, and infectious diseases.
