  We define the concept of weak pseudotwistor for an algebra $(A, \mu)$ in a
monoidal category $\mathcal{C}$, as a morphism $T:A\otimes A\rightarrow
A\otimes A$ in $\mathcal{C}$, satisfying some axioms ensuring that $(A, \mu
\circ T)$ is also an algebra in $\mathcal{C}$. 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.
