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Related lectures (13)

Introduction to Adjunctions in Category Theory

Introduces adjunctions in category theory, exploring necessary conditions and natural transformations for adjoint functors.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Limits and Colimits: Equalizers and Coequalizers

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Lifting properties, Chapter 2(a): Definition and elementary properties of model categories

Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.

Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Homotopical Algebra: Introduction

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

Quasicategories: An Alternative Homotopy Theory

Introduces quasicategories as an alternative approach to defining homotopy maps and categories.

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.

Model Categories and Homotopy Theory: Functorial Connections

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

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

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