An infinite loop space structure for K-theory of bimonoidal categories

• Main Author: Osorno, Angélica María
• Other Authors: Mark Behrens.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2010
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/60104

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Cataloged from student-submitted PDF version of thesis. === Includes bibliographical references (p. 63-64). === In recent work of Baas-Dundas-Richter-Rognes, the authors introduce the notion of the K- theory of a bimonoidal category R, and show that it is equivalent to the algebraic K-theory space of the ring spectrum KR. In this thesis we show that K(R) is the group completion of the classifying space of the 2-category ModR of modules over R, and show that ModR is a symmetric monoidal 2-category. We explain how to use this symmetric monoidal structure to produce a [Gamma]-(2-category), which gives an infinite loop space structure on K(R). We show that the equivalence mentioned above is an equivalence of infinite loop spaces. === by Angélica María Osorno. === Ph.D.