
The algebra of Kleene stars of the plane and polylogarithms
We extend the definition and study the algebraic properties of the polyl...
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On the Behaviour of Coalgebras with Side Effects and Algebras with Effectful Iteration
For every finitary monad T on sets and every endofunctor F on the catego...
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The language (and series) of Hammersleytype processes
We study languages and formal power series associated to (variants of) H...
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Automatic sequences: from rational bases to trees
The nth term of an automatic sequence is the output of a deterministic f...
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Automata Learning: An Algebraic Approach
We propose a generic categorical framework for learning unknown formal l...
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Domain Theory in Constructive and Predicative Univalent Foundations
We develop domain theory in constructive univalent foundations without V...
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Kleene stars of the plane, polylogarithms and symmetries
We extend the definition and construct several bases for polylogarithms ...
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A New Foundation for Finitary Corecursion and Iterative Algebras
This paper contributes to a theory of the behaviour of "finitestate" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to a new fixpoint of the coalgebraic type functor called locally finite fixpoint (LFF). We prove that if the given endofunctor preserves monomorphisms then the LFF always exists and is a subcoalgebra of the final coalgebra (unlike the rational fixpoint previously studied by Adámek, Milius, and Velebil). Moreover, we show that the LFF is characterized by two universal properties: (1) as the final locally finitely generated coalgebra, and (2) as the initial fgiterative algebra. As instances of the LFF we first obtain the known instances of the rational fixpoint, e.g. regular languages, rational streams and formal powerseries, regular trees etc. And we obtain a number of new examples, e.g. (realtime deterministic resp. nondeterministic) contextfree languages, constructively Salgebraic formal powerseries (and any other instance of the generalized powerset construction by Silva, Bonchi, Bonsangue, and Rutten) and the monad of Courcelle's algebraic trees.
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