Homotopical Algebra

Related lectures (32)

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

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Covers group quotient, group actions, and functors connecting sets and G-sets.

Introduces functors, including identity and forgetful functors, and explores duality functors.

Explores functors between categories and the conditions for left and right adjoints.

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Provides an overview of categories, functors, and natural transformations in mathematics.

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

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