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Section (category theory)
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Limits and Colimits: Understanding Categories
Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.
Group Quotients and Push-outs
Explores group quotients and push-outs, discussing isomorphisms and surjectivity in different scenarios.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes, including path object construction and fibrations.
Homotopy Lifting
Explains homotopy lifting, paths, proofs, constant paths, discrete spaces, and monomorphisms.
Lifting properties and model categories
Covers the study of lifting properties in categories, focusing on the left and right lifting properties.
Introduction to Category Theory
Covers the introduction to categories, including definitions and examples.
Fixed Points and Orbits Analysis: Group Actions
Explores the definition of orbits and fixed points of a G-object in any category, focusing on G-equivariant applications.
Mutually Inverse Alpha and Beta
Explores adjunctions and mutual inverses alpha and beta in category theory.
Natural Transformations and Functors
Covers natural transformations, functors, and their composition properties in category theory.
Group Actions and Functors
Covers group quotient, group actions, and functors connecting sets and G-sets.
