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- Adriana Balan, Alexander Kurz
- Electr. Notes Theor. Comput. Sci.
- 2010

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)

- Adriana Balan, Alexander Kurz
- CALCO
- 2011

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)

- Adriana Balan, Alexander Kurz, Jiri Velebil
- Logical Methods in Computer Science
- 2013

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, Alexander Kurz, Jiri Velebil
- CALCO
- 2015

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)

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