A weighty theorem of the heart for the algebraic K-theory of higher categories

We introduce the notion of a bounded weight structure on a stable [infinity symbol]-category and prove a generalization of Waldhausen’s sphere theorem for the algebraic K-theory of higher categories. The algebraic K-theory of a stable [infinity symbol]-category with a bounded non-degenerate weight structure is proven to be equivalent to the algebraic K-theory of the heart of the weight structure. We relate this theorem to previous results as well as new applications.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The University of Texas at Austin

Year dc:date.issued

2017

Author dc:creator

• Fontes, Ernest Eugene

Advisor dc:contributor.advisor

• Blumberg, Andrew J.

Committee members dc:contributor.committeemember

• Barwick, Clark
• Ben-Zvi, David
• Neitzke, Andrew

• Algebraic K-theory
• Homotopy theory
• Category theory
• Algebraic topology

Language dc:language.iso

en

Identifier

doi:10.15781/T29S1M210

OAI identifier oai:identifier

oai:repositories.lib.utexas.edu:2152/62096