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1. McBride, Aaron. Grothendieck Group Decategorifications and Derived Abelian Categories .

Degree: 2015, University of Ottawa

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

…Ab from the category of essentially small exact categories (whose morphisms are exact… …decategorifications, a background in additive, abelian, exact and triangulated categories is required. To… …Grothendieck groups. Given a left exact functor F : A → B between abelian categories, we have an… …Categories This chapter provides a brief introduction to additive, abelian, exact, and triangulated… …basic building block for abelian, exact, and triangulated categories. Let us piece together… 

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APA (6th Edition):

McBride, A. (2015). Grothendieck Group Decategorifications and Derived Abelian Categories . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/33000

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

McBride, Aaron. “Grothendieck Group Decategorifications and Derived Abelian Categories .” 2015. Thesis, University of Ottawa. Accessed August 18, 2019. http://hdl.handle.net/10393/33000.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

McBride, Aaron. “Grothendieck Group Decategorifications and Derived Abelian Categories .” 2015. Web. 18 Aug 2019.

Vancouver:

McBride A. Grothendieck Group Decategorifications and Derived Abelian Categories . [Internet] [Thesis]. University of Ottawa; 2015. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/10393/33000.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McBride A. Grothendieck Group Decategorifications and Derived Abelian Categories . [Thesis]. University of Ottawa; 2015. Available from: http://hdl.handle.net/10393/33000

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.