2026-09-19T01:14:27Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/601042022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Mark Behrens.
Osorno, Angélica María
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2010-12-06T16:37:18Z
2010-12-06T16:37:18Z
2010
2010
http://hdl.handle.net/1721.1/60104
679677768
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.
64 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
An infinite loop space structure for K-theory of bimonoidal categories
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="f7495cb0-545c-4fa9-ab18-c42a2f5fc60b">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>An infinite loop space structure for K-theory of bimonoidal categories</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2010</PublicationDate>
<Authors>
<Author>
<DisplayName>Osorno, Angélica María</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<Abstract>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>