Date of Award
1-1-2018
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
College/School/Department
Department of Mathematics and Statistics
Content Description
1 online resource (ii, iv, 74 pages) : illustrations.
Dissertation/Thesis Chair
Boris Goldfarb
Committee Members
Alexandre Tchernev
Keywords
Algebraic spaces, K-theory, Algebraic topology, Metric spaces, Functions of bounded variation
Subject Categories
Physical Sciences and Mathematics
Abstract
Bounded algebra methods have been a valuable tool in algebraic topology and algebraic K-theory since their introduction in the 1960's. Using two parameters, a metric space and an additive category, Pedersen-Weibel used bounded algebra to produce a non-connective delooping of the K-theory spectrum of a ring. This dissertation generalizes the Pedersen-Weibel construction in the categorical parameter, establishes an embedding of the Pedersen-Weibel construction into the generalized bounded category, and proves the analogue of nonconnective delooping theorem for this embedding.
Recommended Citation
Bennett, Bryan, "Bounded algebra in symmetric monoidal categories" (2018). Legacy Theses & Dissertations (2009 - 2024). 2002.
https://scholarsarchive.library.albany.edu/legacy-etd/2002