On Covariety Lattices
نویسنده
چکیده
This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice LCV(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 Pκ-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 LCV(K) is isomorphic to the lattice (τ,∪,∩) of open sets of τ .
منابع مشابه
Covarieties of Coalgebras: Comonads and Coequations
Coalgebras provide effective models of data structures and state-transition systems. A virtual covariety is a class of coalgebras closed under coproducts, images of coalgebraic morphisms, and subcoalgebras defined by split equalisers. A covariety has the stronger property of closure under all subcoalgebras, and is behavioural if it is closed under domains of morphisms, or equivalently under ima...
متن کاملA characterization of multiwavelet packets on general lattices
The objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $Gamma$ in $mathbb R^d$ by virtue of time-frequency analysis, matrix theory and operator theory.
متن کاملTopological Residuated Lattices
In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...
متن کاملSome results on $L$-complete lattices
The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...
متن کاملOn generalized topological molecular lattices
In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices, topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...
متن کامل