This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice 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 -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 is isomorphic to the lattice (τ,∪,∩) of open sets of τ.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1142,
author = {Tomasz Brengos},
title = {On covariety lattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {28},
year = {2008},
pages = {179-191},
zbl = {1203.08003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1142}
}
Tomasz Brengos. On covariety lattices. Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008) pp. 179-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1142/
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