Homotopical Algebra: Introduction

Related lectures (32)

Page 3 of 4

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

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

Explores natural transformations in algebra, defining functors and isomorphisms.

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.

Explores lifting properties and model categories in topological spaces.

Explores sets of left homotopy equivalence classes of morphisms in model categories.

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

Covers induced homomorphisms on relative homology groups and their properties.

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.