Homotopy Categories: Model Structures

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Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Model Categories and Homotopy Theory: Functorial Connections

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

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Examples, Chapter 1(b): Adjunctions

Presents concrete examples of adjunctions between Set and Top categories.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

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.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Group Actions: Quotients and Homomorphisms

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

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

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