
Algebraic cocompleteness and finitary functors
A number of categories is presented that are algebraically complete and ...
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On free completely iterative algebras
For every finitary set functor F we demonstrate that free algebras carry...
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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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Toward an Algebraic Theory of Systems
We propose the concept of a system algebra with a parallel composition o...
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Reflecting Algebraically Compact Functors
A compact Talgebra is an initial Talgebra whose inverse is a final Tc...
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Relating Apartness and Bisimulation
A bisimulation for a coalgebra of a functor on the category of sets can ...
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Some Open Problems related to Creative Telescoping
Creative telescoping is the method of choice for obtaining information a...
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A canonical algebra of open transition systems
Feedback and state are closely interrelated concepts. Categories with feedback, originally proposed by Katis, Sabadini and Walters, are a weakening of the notion of traced monoidal categories, with several pertinent applications in computer science. The construction of the free such categories has appeared in several different contexts, and can be considered as state bootstrapping. We show that a categorical algebra for open transition systems, ππ©ππ§(ππ«ππ©π‘)_β, also due to Katis, Sabadini and Walters, is the free category with feedback over ππ©ππ§(πππ). Intuitively, this algebra of transition systems is obtained by adding state to an algebra of predicates, and therefore ππ©ππ§(ππ«ππ©π‘)_β is, in this sense, the canonical such algebra.
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