It is known that the category of Waldhausen categories is a closed symmetric multicategory and algebraic K-theory is a multifunctor from the category of Waldhuasen categories to the category of spectra. By assigning to any Waldhausen category the fundamental groupoid of the 1-type of its K-theory spectrum, we get a functor from the category of Waldhausen categories to the category of Picard groupoids, since stable 1-types are classified by Picard groupoids. We prove that this functor is a multifunctor to a corresponding multicategory of Picard groupoids. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / April 10, 2018. / closed structure, K-theory, multifunctor, Picard groupoid, Stable quadratic modules, Waldhausen / Includes bibliographical references. / Ettore Aldrovandi, Professor Directing Dissertation; John Rawling, University Representative; Amod Agashe, Committee Member; Paolo Aluffi, Committee Member; Kate Petersen, Committee Member; Mark van Hoeij, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_653520 |
| Contributors | Valdes, Yaineli (author), Aldrovandi, Ettore (professor directing dissertation), Rawling, John Piers (university representative), Agashe, Amod S. (committee member), Aluffi, Paolo, 1960- (committee member), Petersen, Kathleen L. (committee member), Hoeij, Mark van (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (60 pages), computer, application/pdf |
Page generated in 0.0021 seconds