Abstract
In this thesis, the classical diagram lemmas of homological algebra, as well as a few new ones, are formulated and proved in a self-dual context introduced by A. Goswami and Z. Janelidze, which covers all group-like structures. Among the new diagram lemmas is a generalized formulation of the snail lemma. We also give examples of diagram lemmas for finite cyclic groups and show that in all cases that we consider, they simplify to a certain canonical form. Using a computer program we then count the number of concrete instances of these diagram lemmas, arriving to new integer sequences. Further exploration of the new insights coming from this part of the thesis is left for future work. The thesis also has an expository part where we give complete proofs of the general toolkit for working in the above-mentioned self-dual context, and provide a detailed verification that the context is applicable to non-abelian groups, and more generally, Słomi´nski algebras.
M.Sc. (Chemistry)