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kleene_algebras [2010/07/29 18:30] 127.0.0.1 external edit |
kleene_algebras [2010/09/04 17:00] (current) jipsen |
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==Morphisms== | ==Morphisms== | ||
Let $\mathbf{A}$ and $\mathbf{B}$ be Kleene algebras. | Let $\mathbf{A}$ and $\mathbf{B}$ be Kleene algebras. | ||
- | A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:Aarrow B$ that is a | + | A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\to B$ that is a |
homomorphism: $h(x\vee y)=h(x)\vee h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(x^{\ast })=h(x)^{\ast }$, $h(0)=0$, | homomorphism: $h(x\vee y)=h(x)\vee h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(x^{\ast })=h(x)^{\ast }$, $h(0)=0$, | ||
and $h(1)=1$. | and $h(1)=1$. | ||
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====Basic results==== | ====Basic results==== | ||
- | [[Kleene algebras (otter)]] | ||
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^[[Strong amalgamation property]] | | | ^[[Strong amalgamation property]] | | | ||
^[[Epimorphisms are surjective]] | | | ^[[Epimorphisms are surjective]] | | | ||
+ | |||
====Finite members==== | ====Finite members==== | ||
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[[Kleene lattices]] | [[Kleene lattices]] | ||
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====Superclasses==== | ====Superclasses==== |
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