Egghe's continuous information production processes (in short IPP's) are described using category theory. Therefore, we first review the main ingredients of this mathematical theory, introduced byEilenberg andMac Lane more than four decades ago. Then we show how the notion of duality, as used byEgghe, can be placed in the abstract framework of categorical duality. This leads to a natural isomorphism involving the identity functor on a category of continuous IPP's. This natural isomorphism is completely similar to the well-known natural isomorphism between a finite-dimensional vector space and its double dual. We further show that to develop Egghe's theory on IPP's one needs no other intervals than the unit interval.