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Title Grothendieck Group Decategorifications and Derived Abelian Categories
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Publication Date
Date Accessioned
University/Publisher University of Ottawa
Abstract 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.
Subjects/Keywords additive categories; abelian categories; exact categories; triangulated categories; Grothendieck groups; category theory; cochain complexes; homotopy category; cohomology; bounded derived category; derived functors
Language en
Country of Publication ca
Record ID handle:10393/33000
Repository ottawa
Date Indexed 2018-01-03
Issued Date 2015-01-01 00:00:00

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