On coalgebras and type transformations

• Autorzy: H. Peter Gumm
• Języki publikacji: EN

Abstrakty

EN

We show that for an arbitrary Set-endofunctor T the generalized membership function given by a sub-cartesian transformation μ from T to the filter functor 𝔽 can be alternatively defined by the collection of subcoalgebras of constant T-coalgebras. Sub-natural transformations ε between any two functors S and T are shown to be sub-cartesian if and only if they respect μ. The class of T-coalgebras whose structure map factors through ε is shown to be a covariety if ε is a natural and sub-cartesian mono-transformation.

Słowa kluczowe

EN

coalgebra; endofunctor; filter functor; cartesian transformation; crisp

Kategorie tematyczne

• 68Q85: Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
• 18C10: Theories (e.g. algebraic theories), structure, and semantics
• 68Q10: Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2007
• Tom: 27
• Numer: 2
• Strony: 187-197

Daty

wydano

2007

otrzymano

2006-05-01

poprawiono

2006-07-25

Twórcy

autor

H. Peter Gumm

• Philipps-University Marburg, Faculty of Mathematics and Computer Science, Hans-Meerwein-Straße 35032 Marburg, Germany

Bibliografia

• [1] P. Aczel and N. Mendler, A final coalgebra theorem, pp. 357-365 in: D.H. Pitt et al., eds, Proceedings Category Theory and Computer Science, Lecture Notes in Computer Science, Springer 1989.
• [2] S. Awodey, Category Theory, Oxford University Press (2006).
• [3] H.P. Gumm, Birkhoff's variety theorem for coalgebras, Contributions to General Algebra 13 (2000), 159-173.
• [4] H.P. Gumm, Functors for coalgebras, Algebra Universalis 45 (2001), 135-147.
• [5] H.P. Gumm, From{T-coalgebras to filter structures and transition systems, pp. 194-212 in: D.H. Fiadeiro et al., eds, Algebra and Coalgebra in Computer Science, vol 3629 of Lecture Notes in Computer Science, Springer 2005.
• [6] H.P. Gumm and T. Schröder, Coalgebras of bounded type, Math. Struct. in Comp. Science 12 (2001), 565-578.
• [7] H.P. Gumm and T. Schröder, Types and coalgebraic structure, Algebra Universalis 53 (2005), 229-252.
• [8] E.G. Manes, Implementing collection classes with monads, Math. Struct. in Comp. Science 8 (1998), 231-276.
• [9] J.J.M.M. Rutten, Universal coalgebra: a theory of systems, Theoretical Computer Science 249 (2000), 3-80.
• [10] J.D.H. Smith, Permutation representations of left quasigroups, Algebra Universalis 55 (2006), 387-406.

Identyfikatory

DOI

10.7151/dmgaa.1126