We define firm semigroups and firm acts as non-additive analogues of firm rings and firm
modules. Using the categories of firm acts we develop Morita theory for firm semigroups. We …

An n× n matrix factorization of a polynomial f is a pair of n× n matrices (P, Q) such that PQ= f
In, where In is the n× n identity matrix. In this dissertation, we study matrix factorizations of an …

We characterize abstract Morita contexts in several bicategories. In particular, we use
heteromorphisms for the bicategory Prof of categories and profunctors and coreflective …

We use a matrix approach to study the concept of Morita context in the bicategory $\mathcal
{LG} _ {K} $ of Landau-Ginzburg models on a particular class of objects. In fact, we first use …

We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory,
generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way …

In this paper we study Morita contexts between rings without identity. We prove that if two
associative rings are connected by a Morita context with surjective mappings, then these …

Monads are well known to be equivalent to lax functors out of the terminal category. Morita
contexts are here shown to be lax functors out of the chaotic category with two objects. This …

Abstract The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads
are described. More specifically, a notion of a Morita context comprising of two monads, two …

A basic theory of cowreath or extended distributive laws in the bicategory of unital
bimodules, is deciphered. Precisely, we give in terms of tensor product over a scalar base …

The classical result in the theory of unital rings that the maps of a Morita context are
isomorphisms when they are epimorphisms can be proven in the general setting of wide …