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sav08:mapping_fixpoints_under_lattice_morphisms [2009/03/26 13:50] vkuncak |
sav08:mapping_fixpoints_under_lattice_morphisms [2009/03/26 13:51] vkuncak |
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====== Mapping Fixpoints Under Lattice Morphisms ====== | ====== Mapping Fixpoints Under Lattice Morphisms ====== | ||
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+ | **Definition:** Let $(X,\le)$ and $(Y,\sqsubseteq)$ be complete [[lattices]]. We call and $F : X \to Y$ a function. We ca | ||
**Lemma:** Let $(X,\le)$ and $(Y,\sqsubseteq)$ be complete lattices, and $F : X \to X$, $\Gamma : X \to Y$, $F^\# : Y \to Y$ be complete morphisms (they distribute through arbitrary least upper bound) such that | **Lemma:** Let $(X,\le)$ and $(Y,\sqsubseteq)$ be complete lattices, and $F : X \to X$, $\Gamma : X \to Y$, $F^\# : Y \to Y$ be complete morphisms (they distribute through arbitrary least upper bound) such that |