# Differences

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semilattices [2020/03/24 16:13] pnotthesamejipsen |
semilattices [2020/03/24 17:24] (current) pnotthesamejipsen |
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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==== |

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