Existence of Left Derived Functors: Part 2

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Why Quasicategories?

Discusses the benefits of quasi-category theory and model structures.

Model Category: Definition and Elementary Properties

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

Quillen Equivalences

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

Homotopical Algebra: Introduction

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

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.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Sets of Left Homotopy Classes: The Homotopy Relation in a Model Category

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

Homotopy Theory in Care Complexes

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Introduction to Left Homotopy: The Homotopy Relation in a Model Category

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