Cameron Wright
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SIG 228
Title: Homological Algebra in Non-Abelian Contexts
Abstract: After a brief review of abelian categories, we examine exact categories and some aspects of their homological algebra. In particular, we consider complexes and the construction of the derived category, emphasizing the fundamental pieces of machinery that allow for this construction. Subsequently, we move on to see some examples of homological algebra in non-additive settings, where we will see that some of our favorite toys are now broken. We then survey some approaches to remedying the situation. This final portion has connections with tropical geometry, F1-geometry, and matroid theory.