Elementary Properties of Model Categories

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Serre model structure: Left and right homotopy

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

Homotopical Algebra: Introduction

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

Quillen Equivalences

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

Model Categories and Homotopy Theory: Functorial Connections

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

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 Categories: Model Structures

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Derived Functors in Homotopical Algebra

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

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.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.