Necessary conditions for the existence of Morita Contexts in the bicategory of Landau-Ginzburg Models

Abstract

We use a matrix approach to study the concept of Morita context in the bicategory ${\mathcal{L}\mathcal{G}}_K$ of Landau-Ginzburg models on a particular class of objects. In fact, we first use properties of matrix factorizations to state and prove two necessary conditions to obtain a Morita context between two objects of ${\mathcal{L}\mathcal{G}}_K$. Next, we use a celebrated result (due to Schur) on determinants of block matrices to show that these necessary conditions are not sufficient. Finally, we state a trivial sufficient condition.

23 pages

References in corpus (1)

• Wide Morita contexts in Bicategories

Cited by in corpus (1)

• Some applications of the multiplicative tensor product of matrix factorizations