Geodesic
On covariety lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 179-191

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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.
Keywords: coalgebra, covariety, coalgebraic logic 
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Brengos, Tomasz. On covariety lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 179-191. http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a3/