Two Cartesian closed categories of information algebras

•We present an equivalent characterization of continuous information algebras.•The set of all continuous mappings on continuous information algebras is continuous.•The two categories COMP and CON are both Cartesian closed.

The compact information algebra and the continuous information algebra are two special information algebras, which are algebraic structures modeling computation in many different contexts. We show that the set of all continuous mappings between two continuous information algebras also forms a continuous information algebra. Further, we obtain that the two categories COMP and CON, consisting of compact information algebras and continuous information algebras as objects respectively, continuous mappings as morphisms, are both Cartesian closed.