Properties of Cartesian Products and Disjoint Unions

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Page 3 of 4

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Explores coproducts, universal properties, and natural transformations in category theory.

Introduces the basics of group theory, defining groups, categories, and groupoids.

Covers natural transformations between functors, identity transformations, and equivalence of categories.

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

Covers examples of relation composition, Cartesian product, and injective functions.

Introduces sets, Cartesian product, order importance, and relations on sets.

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