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Full text release has been delayed at the author's request until August 08, 2024

ETD Abstract Container

Abstract Header

Characterization of Unitary Braided-Enriched Monoidal Categories

Dell, Zachary Ryan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1657825586731435

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Mathematics.
Categories enriched over a monoidal category V form a 2-category. Under standard additional assumptions, we prove a 2-equivalence between this and the 2-category of module categories over V. Going up one categorial level, when V is braided monoidal, we prove the same result in the case of rigid V-monoidal categories and rigid V-module monoidal categories. Braided-enriched monoidal categories arise in settings such as topologically ordered systems in theoretical condensed matter physics. Many of these settings are unitary, yet previously there was no general concept of enriched unitarity. After providing a definition of a dagger V-category, we extend the 2-equivalences above to the unitary setting.
David Penneys (Advisor)
Niles Johnson (Committee Member)
Thomas Kerler (Committee Member)
79 p.
Mathematics
enriched categories; braided enriched categories; unitary enriched categories; enriched monoidal categories; module categories; unitary module categories

Recommended Citations

Citations

  • Dell, Z. R. (2022). Characterization of Unitary Braided-Enriched Monoidal Categories [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1657825586731435

    APA Style (7th edition)

  • Dell, Zachary. Characterization of Unitary Braided-Enriched Monoidal Categories. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1657825586731435.

    MLA Style (8th edition)

  • Dell, Zachary. "Characterization of Unitary Braided-Enriched Monoidal Categories." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1657825586731435

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.