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semilattices [2020/03/24 16:13]
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semilattices [2020/03/24 17:24] (current)
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This definition shows that semilattices form a variety. This definition shows that semilattices form a variety.
 +==Morphisms==
 +Let $\mathbf{S}$ and $\mathbf{T}$ be semilattices. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\to T$ that is a homomorphism:
 +
 +$h(xy)=h(x)h(y)$
====Definition==== ====Definition====
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$x\wedge y$ is the greatest lower bound of $\{x,y\}$. $x\wedge y$ is the greatest lower bound of $\{x,y\}$.
-==Morphisms== 
-Let $\mathbf{S}$ and $\mathbf{T}$ be semilattices. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:Sarrow T$ that is a homomorphism:  
- 
-$h(xy)=h(x)h(y)$ 
====Examples==== ====Examples====