Adriana Balan

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We extend Barr's well-known characterization of the final coalgebra of a Set-endofunctor H as the completion of its initial algebra to the Eilenberg-Moore category Alg(M) of algebras associated to a Set-monad M, if H can be lifted to Alg(M). As further analysis, we introduce the notion of commuting pair of endofunctors (T, H) with respect to a monad M and(More)
Motivation Most of coalgebraic logic is focussed on Set-coalgebras and their associated (Boolean) logics. Investigation of coalgebraic logic over Poset already started – expressivity results [Kurz-Kapulkin-Velebil CMCS2010]. Would deserve a systematic investigation of Poset-functors and their coalgebras. In this talk: we restrict on how to move from(More)
The notions of Galois and cleft extensions are generalized for coquasi-Hopf algebras. It is shown that such an extension over a coquasi-Hopf algebra is cleft if and only if it is Galois and has the normal basis property. A Schneider type theorem ([33]) is proven for coquasi-Hopf algebras with bijective antipode. As an application, we generalize(More)
A certain generalisation of the hierarchy of mKdV equations (modified KdV), which forms an integrable system, is studied here. This generalisation is based on a Lax operator associated to the equations, with principal components of degrees between −3 and 0. The results are the following ones: 1) an isomorphism between the space of jets of the system and a(More)
We study a generalization of the hierarchy of mKdV equations (modi-ed KdV), which forms an integrable system. This generalization is based on a Lax operator associated to the equations, with principal components of degrees between ?3 and 0. The main result of the study is the com-mutation of the classical integrals of motion. For that purpose, one can(More)
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