Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.
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.
