We define the concept of weak pseudotwistor for an algebra (A,μ) in a
monoidal category C, as a morphism T:A⊗A→A⊗A in C, satisfying some axioms ensuring that (A,μ∘T) is also an algebra in C. This concept generalizes the
previous proposal called pseudotwistor and covers a number of exemples of
twisted algebras that cannot be covered by pseudotwistors, mainly examples
provided by Rota-Baxter operators and some of their relatives (such as Leroux's
TD-operators and Reynolds operators). By using weak pseudotwistors, we
introduce an equivalence relation (called "twist equivalence") for algebras in
a given monoidal category.Comment: 15 pages; continues arXiv:math/0605086 and arXiv:0801.2055, some
concepts from these papers are recalled; we added a Note and some references.
In this final version, accepted for publication in J. Algebra Appl., the
title has been slighty modified and few little things have been adde