Terminal coalgebras in well-founded set theory
Theoretical Computer Science
A small final coalgebra theorem
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
On abstract data types presented by multiequations
Theoretical Computer Science
Automata and Algebras in Categories
Automata and Algebras in Categories
Category Theory and Computer Science
On varieties and covarieties in a category
Mathematical Structures in Computer Science
On varieties and covarieties in a category
Mathematical Structures in Computer Science
Theoretical Computer Science - Logic, semantics and theory of programming
A general final coalgebra theorem
Mathematical Structures in Computer Science
Terminal coalgebras and free iterative theories
Information and Computation
Mathematical Structures in Computer Science
The category-theoretic solution of recursive program schemes
Theoretical Computer Science - Algebra and coalgebra in computer science
Coequational Logic for Finitary Functors
Electronic Notes in Theoretical Computer Science (ENTCS)
Rank-1 modal logics are coalgebraic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Coequational logic for accessible functors
Information and Computation
From grammars and automata to algebras and coalgebras
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
The category theoretic solution of recursive program schemes
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
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For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra At. The universal property of this family of coalgebras, resembling freeness, is that for every state s of every system S there exists a unique coalgebra homomorphism from a unique At which takes the root of t to s. Consequently, the tree coalgebras are finitely presentable and form a strong generator. Thus, these categories of coalgebras are locally finitely presentable; in particular every system is a filtered colimit of finitely presentable systems.In contrast, for transition systems expressed as coalgebras over the finite-power-set functor we show that there are systems which fail to be filtered colimits of finitely presentable (=finite) ones.Surprisingly, if λ is an uncountable cardinal, then λ-presentation is always well-behaved: whenever an endofunctor F preserves λ-filtered colimits (i.e., is λ-accessible), then λ-presentable coalgebras are precisely those whose underlying objects are λ-presentable. Consequently, every F coalgebra is a λ-filtered colimit of λ-presentable coalgebras; thus Coalg F is a locally λ-presentable category. (This holds for all endofunctors of λ-accessible categories with colimits of ω-chains.) Corollary: A set functor is bounded at λ in: the sense of Kawahara and Mori iff it is λ+-accessible.