| Popis: |
In this thesis we describe a new version of acyclic models, which was first given by Barr, that gives the Theorem of Barr and Beck, and of Andre as special cases. We begin the thesis with Beck's definition of module and we describe how he used this definition, in conjunction with the theory of triples, to define homology theories. The theory described here is based on the notion of acyclic classes. An acyclic class is a class of objects in a category of chain complexes and corresponds to a class of arrows, whose mapping cones they are. We also give an answer to the question, where do acyclic classes come from. We conclude the thesis by showing that Cartan-Eilenberg cohomology of groups, of associative algebras, and of Lie algebras are the same as cotriple ones, using proofs based on those presented by Barr. |
