Homotopy category

Formal sciences
Mathematics
Topology
Algebraic topology

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Geometric Realization in Model Categories

Explores geometric realization, simplicial sets, and model category structures.

Quasi-Categories: Active Learning Session

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.

Existence of Left Derived Functors: Part 2

Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.

CW Approximation Uniqueness

Explores the uniqueness of CW approximation and Whitehead's theorem through the construction of maps inducing isomorphisms on homotopic groups.

Universal Covering Construction

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Characterizing Fibrations in Chain Complexes

Explores the characterization of fibrations and acyclic fibrations in chain complexes.

Homotopical Algebra: The Homotopy Category of a Model Category

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

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.