Definition:Frame Homomorphism

Definition

Let $L_1 = \struct{S_1, \preceq_1}$ and $L_2 = \struct{S_2, \preceq_2}$ be frames.

Let $\phi: S_1 \to S_2$ be a mapping between the underlying sets of $L_1$ and $L_2$.

Then:

$\phi$ is a frame homomorphism, denoted $\phi: L_1 \to L_2$

if and only if:

$\phi$ is finite meet preserving and arbitrary join preserving

Also see

• Definition:Continuous Map (Locale)

Sources

• 1982: Peter T. Johnstone: Stone Spaces: Chapter II: Introduction to Locales, $\S1.1$ Definition (a)