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The embedding of initial algebras into dialgebras

Published 23 Jan 2026 in math.RA | (2601.16619v1)

Abstract: In this paper, for a given variety $\Var$, we present a universal algorithm that constructs a subvariety of $\Var$-dialgebras from which one can recover an algebra belonging to $\Var$. We call such a variety an initial $\Var$-dialgebra. In addition, we construct the basis of the free initial Lie and associative dialgebras.

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