Lifting Properties in Model Categories: An Overview

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Covers simplicial and cosimplicial objects in category theory with practical examples.

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

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.