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.
Covers the construction of a left adjoint to the singular set functor, comparing the homotopy theory of topological spaces with that of simplicial sets.
Explores higher-order interactions in brain networks using simplicial complexes and information theory, analyzing data from fMRI, financial time-series, and infectious diseases.
Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.
Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.
