Algebras and their bimodules form a 2-category in which 2-morphisms are certain zero-th Hochschild cohomology groups. When we derive this structure (i.e., use Hochschild cochains instead of HH^0 for 2-morphisms), we find that algebras form a category in dg cocategories. The Hochschild-Kostant-Rosenberg theorem and non-commutative calculus give a rich algebraic structure on Hochschild cohomology along with Hochschild homology. When incorporating the structure on Hochschild homology, we find that algebras form a 2-category with a trace functor. Deriving this again, we conclude that algebras form a category in dg cocategories with a trace functor up to homotopy.

Last modified

• 03/13/2018

Creator

• Ann Rebecca Wei

DOI

• https://doi.org/10.21985/N2XH5Z

Subject

• Mathematics

Keyword

• Mathematics
• Algebra

Date created

• 2017-01-01

Resource type

• Dissertation

Rights statement

• In Copyright