# On covariety lattices

Discussiones Mathematicae - General Algebra and Applications (2008)

- Volume: 28, Issue: 2, page 179-191
- ISSN: 1509-9415

## Access Full Article

top## Abstract

top## How to cite

topTomasz Brengos. "On covariety lattices." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 179-191. <http://eudml.org/doc/276935>.

@article{TomaszBrengos2008,

abstract = {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.},

author = {Tomasz Brengos},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {coalgebra; covariety; coalgebraic logic},

language = {eng},

number = {2},

pages = {179-191},

title = {On covariety lattices},

url = {http://eudml.org/doc/276935},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Tomasz Brengos

TI - On covariety lattices

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2008

VL - 28

IS - 2

SP - 179

EP - 191

AB - 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.

LA - eng

KW - coalgebra; covariety; coalgebraic logic

UR - http://eudml.org/doc/276935

ER -

## References

top- [1] M. Barr, Terminal Coalgebras in Well-founded Set Theory, Theoretical Computer Science 144 (2) (1993), 299-315. Zbl0779.18004
- [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. Zbl0982.08003
- [4] H.P. Gumm and T. Schröder, Coalgebras of bounded type, Mathematical Structures in Computer Science 12 (5) (2002), 565-578. Zbl1011.08009
- [5] H.P. Gumm, From T-coalgebras to filter structures and transtion systems, CALCO 2005, Springer Lecture Notes in Computer Science (LNCS) 3629, 2005. Zbl1151.18001

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.