Bilinear factorization of algebras
Year: 2011
Type: article
Abstract: We study the (so-called bilinear) factorization problem answered by a weak wreath product (of monads and, more specifically, of algebras over a commutative ring) in the works by Street and by Caenepeel and De Groot. A bilinear factorization of a monad R turns out to be given by monad morphisms A --> R R. We prove a biequivalence between the bicategory of weak distributive laws and an appropriately defined bicategory of bilinear factorization structures. As an illustration of the theory, we collect some examples of algebras over commutative rings which admit a bilinear factorization; i.e. which arise as weak wreath products.
Authors: Böhm, Gabriella, Gómez-Torrecillas, José
Institutions: Hungarian Academy of Sciences, Universidad de Granada
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963535114