Introduction to Category Theory: Adjoint Functors

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Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

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Introduces limits and colimits in a category, covering their properties and uniqueness.

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.

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Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

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

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Explores group actions, defining functors on groups, and verifying properties of group actions.

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Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

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Introduces natural transformations through examples, covering equivalence of categories and functor properties.