my beamer presentation - Departament de matemà tiques

Outline
Definitions and examples
Homological properties of kC-mod
An example
A closed symmetric monoidal category
Adjoint functors and a spectral sequence
Two categorical constructions
Hochschild cohomology
A crash introduction to closed symmetric monoidal
categories
Mac Lane: Much of the force of category theory will be seen to
reside in using categories with specified additional structures.
One basic example will be the closed categories. The simplest
closed symmetric monoidal category is perhaps Vect k .
There is a tensor product − ⊗ k −, which is symmetric.
There exists a tensor identity k.
It is closed in the sense that for a pair of (ordered) spaces
V , W , there is a function object, a.k.a. the internal hom,
Hom k (V , W ) in the category Vect k .
Hom k (U ⊗ k V , W ) ∼ = Hom k (U, Hom k (V , W )).
Fei Xu
Finite category algebras