On covariety lattices

• Autorzy: Tomasz Brengos
• Języki publikacji: EN

Abstrakty

EN

This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice $L_{CV}(K)$ of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a $P_κ$-coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras, such that $L_{CV}(K)$ is isomorphic to the lattice (τ,∪,∩) of open sets of τ.

Słowa kluczowe

EN

coalgebra; covariety; coalgebraic logic

Kategorie tematyczne

• 03C99: None of the above, but in this section
• 03B70: Logic in computer science

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 179-191

Daty

wydano

2008

otrzymano

2007-11-21

poprawiono

2008-03-05

Twórcy

autor

Tomasz Brengos

• Faculty of Mathematics and Information Sciences, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

• [1] M. Barr, Terminal Coalgebras in Well-founded Set Theory, Theoretical Computer Science 144 (2) (1993), 299-315.
• [2] H.P. Gumm, Elements of the General Theory of Coalgebras, LUATCS'99, Rand Africaans University, Johannesburg, South Africa 1999.
• [3] H.P. Gumm, Functors for coalgebras, Algebra Universalis 45 (2-3) (2001), 135-147.
• [4] H.P. Gumm and T. Schröder, Coalgebras of bounded type, Mathematical Structures in Computer Science 12 (5) (2002), 565-578.
• [5] H.P. Gumm, From T-coalgebras to filter structures and transtion systems, CALCO 2005, Springer Lecture Notes in Computer Science (LNCS) 3629, 2005.

Identyfikatory

DOI

10.7151/dmgaa.1142