Homotopical connectivity

Related lectures (32)

Page 3 of 4

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Explores pointed mapping spaces, the exponential law, adjunction properties, and homotopic classes.

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Explores vector fields, potentials, and their relationship, focusing on necessary and sufficient conditions.

Explores the basic properties of left homotopy in model categories, focusing on weak equivalences and morphism relationships.

Explores Green's Theorem application in domain analysis and potential functions.

Explores the proof of the Hurewicz Theorem and its applications to spheres and homotopy groups.

Introduces left homotopy between morphisms and its preservation under postcomposition in a model category.