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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)

Background Modal logic atomic propositions (a ∧ b) = a ∧ b, = ♦(a ∨ b) = ♦a ∨ ♦b, ♦⊥ = ⊥ (⇒ modal operators are monotone) a ∧ ♦b ≤ ♦(a ∧ b) (a ∨ b) ≤ ♦a ∨ b

- Adriana Balan
- 2006

If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we prove that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A H. We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.

- Adriana Balan
- 2008

The notion of crossed product with a coquasi-Hopf algebra H is introduced and studied. The result of such a crossed product is an algebra in the monoidal category of right H-comodules. We give necessary and sufficient conditions for two crossed products to be equivalent. Then, two structure theorems for coquasi Hopf modules are given. First, these are… (More)

- Adriana Balan
- 2008

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)

We show that for a commutative quantale V every functor Set −→ V-cat has an enriched left-Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric. 1 Introduction Coalgebras for a functor T : Set −→ Set capture a wide variety of dynamic… (More)

- A Balan
- 2008

The distribution of prime numbers is here considered. We show a formula for li −1 and we study the π(x) function and Riemann's hypothesis.

- A Balan, Ecole Polytechnique
- 2008

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)

- A Balan
- 1999

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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