Homotopy Theory of Chain Complexes

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

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

Focuses on lifting properties in homotopy theory of chain complexes.

Covers the construction and universal properties of pushouts in group theory.

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

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

Explores natural transformations in algebra, defining functors and isomorphisms.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.