Equivalences for weak crossed products

TL;DR

This paper establishes criteria for when weak crossed products and coproducts are equivalent, simplifying existing conditions and extending the results to biproducts, with applications to known algebraic structures.

Contribution

It provides a new criterion for equivalence of weak crossed products and coproducts, reducing the complexity of previous conditions and extending the theory to biproducts.

Findings

Criteria for equivalence of weak crossed products and coproducts

Conditions for equivalence of weak crossed biproducts

Reduction of conditions in Panaite's results on crossed products

Abstract

In this paper we give a criterion that characterizes equivalent weak crossed products. By duality, we obtain a similar result for weak crossed coproducts and, as a consequence, we find the conditions that assures the equivalence between two weak crossed biproducts. As an application, we show that the main results proved by Panaite, for Brzezi\'nski's crossed products, admits a substantial reduction in the imposed conditions.