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Cohomology of Picard Categories

Horst, Michael
http://rave.ohiolink.edu/etdc/view?acc_num=osu1587396997809887

Abstract Details

2020, Doctor of Philosophy, Ohio State University, Mathematics.
We present a categorification of group cohomology. We do this by replacing all set-based notions with category-based ones. In particular, we use Picard categories in place of Abelian groups. After constructing free Picard categories, we work our way toward (co)chain complexes of Picard categories and the cohomology thereof. We continue by analyzing the homotopical aspects of these complexes, and then defining the derived 2-functors of Picard cohomology. We end by computing specific examples.
Niles Johnson (Advisor)
Sanjeevi Krishnan (Committee Member)
David Penneys (Committee Member)
216 p.
Mathematics

Recommended Citations

Citations

  • Horst, M. (2020). Cohomology of Picard Categories [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587396997809887

    APA Style (7th edition)

  • Horst, Michael. Cohomology of Picard Categories. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1587396997809887.

    MLA Style (8th edition)

  • Horst, Michael. "Cohomology of Picard Categories." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587396997809887

    Chicago Manual of Style (17th edition)

osu1587396997809887
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