On covariety lattices

Tomasz Brengos

Discussiones Mathematicae - General Algebra and Applications (2008)

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

Abstract

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This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice L C V ( 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 C V ( K ) is isomorphic to the lattice (τ,∪,∩) of open sets of τ.

How to cite

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Tomasz 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

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  1. [1] M. Barr, Terminal Coalgebras in Well-founded Set Theory, Theoretical Computer Science 144 (2) (1993), 299-315. Zbl0779.18004
  2. [2] H.P. Gumm, Elements of the General Theory of Coalgebras, LUATCS'99, Rand Africaans University, Johannesburg, South Africa 1999. 
  3. [3] H.P. Gumm, Functors for coalgebras, Algebra Universalis 45 (2-3) (2001), 135-147. Zbl0982.08003
  4. [4] H.P. Gumm and T. Schröder, Coalgebras of bounded type, Mathematical Structures in Computer Science 12 (5) (2002), 565-578. Zbl1011.08009
  5. [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

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