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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]]
 +
====Superclasses==== ====Superclasses====