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Grothendieck Group Decategorifications and Derived Abelian Categories

The Grothendieck group is an interesting invariant of an exact category. It induces a decategorication from the category of essentially small exact categories (whose morphisms are exact functors) to the category of abelian groups. Similarly, the triangulated Grothendieck group induces a decategorication from the category of essentially small triangulated categories (whose morphisms are triangulated functors) to the category of abelian groups. In the case of an essentially small abelian category, its Grothendieck group and the triangulated Grothendieck group of its bounded derived category are isomorphic as groups via a natural map. Because of this, homological algebra and derived functors become useful in surprising ways. This thesis is an expository work that provides an overview of the theory of Grothendieck groups with respect to these decategorications.

Identiferoai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/33000
Date January 2015
CreatorsMcBride, Aaron
ContributorsSavage, Alistair
PublisherUniversité d'Ottawa / University of Ottawa
Source SetsUniversité d’Ottawa
LanguageEnglish
Detected LanguageEnglish
TypeThesis

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