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1-Type of Algebraic K-Theory as a Multifunctor

Title: The 1-Type of Algebraic K-Theory as a Multifunctor.
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Name(s): 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 department
Type of Resource: text
Genre: Text
Doctoral Thesis
Issuance: monographic
Date Issued: 2018
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (60 pages)
Language(s): English
Abstract/Description: 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.
Identifier: 2018_Sp_Valdes_fsu_0071E_14374 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Spring Semester 2018.
Date of Defense: April 10, 2018.
Keywords: closed structure, K-theory, multifunctor, Picard groupoid, Stable quadratic modules, Waldhausen
Bibliography Note: Includes bibliographical references.
Advisory Committee: 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.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/2018_Sp_Valdes_fsu_0071E_14374
Host Institution: FSU

Choose the citation style.
Valdes, Y. (2018). The 1-Type of Algebraic K-Theory as a Multifunctor. Retrieved from http://purl.flvc.org/fsu/fd/2018_Sp_Valdes_fsu_0071E_14374