Triangulated Categories and Matrix Factorizations
MetadataShow full item record
In this thesis we study triangulated categories and look at one specific example, the homotopy category of matrix factorizations. First we define categories and functors. Then we introduce additive and triangulated categories and see that the octahedral axiom can be replaced by Neeman's mapping cone axiom. After this we look at matrix factorizations and the homotopy category of matrix factorizations, HMF(S,x) which leads us to one of our main results, i.e. that HMF(S,x) is triangulated. We prove this with both the octahedral axiom and Neeman's mapping cone theorem. Lastly we look at the homotopy category of totally acyclic complexes over a local, regular ring and see that this is equivalent to HMF(S,x).