$\newcommand\of{\subseteq}\newcommand\N{\mathbb{N}}\newcommand\R{\mathbb{R}}\def\<#1>{\left\langle#1\right\rangle}\newcommand\Z{\mathbb{Z}}\newcommand\Q{\mathbb{Q}}\newcommand\ltomega{{{<}\omega}}\newcommand\unaryminus{-}\newcommand\intersect{\cap}\newcommand\union{\cup}\renewcommand\emptyset{\varnothing}$Let us explore the vast and densely populated expanses of the lattice of all sets of natural…
A complete Heyting algebra is a Heyting algebra which is also a complete lattice; that is, it is a poset with arbitrary limits and colimits, that is also cartesian closed.
By the adjoint functor theorem, one can demonstrate that every frame is a complete Heyting algebra, and vice versa, so far as the underlying poset goes.
However, morphisms of frames needn’t preserve exponential objects or infin…
