Sheafification: Natural Procedure and Adjoints

Related lectures (32)

Page 3 of 4

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.

Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.

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

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Introduces functors in category theory and explains their composition.

Formalizes the construction of orbits and fixed points in group actions, defining morphisms and verifying naturalness.

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

Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.

Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.