Full and faithful functors

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Related lectures (32)

Forgetful functors vs. properties

Explores forgetful functors, properties, and functor categories through examples and discussions.

Functors: Examples

Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.

Lie Algebra Homomorphisms

Explores the association of Lie algebras to algebraic groups and homomorphisms.

Natural Transformations Composition

Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Natural Transformations: Functor L

Explores natural transformations in category theory with a focus on the functor L and its algebraic properties.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Introduction to Derived Functors: Left and Right Derived Functors

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

Review of Simplicial Sets

Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.

Existence of Left Derived Functors

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.

Homotopical Algebra

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

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