Common use of Proposition 4 Clause in Contracts

Proposition 4. 20. Let Ω be a finite set with the discrete topology. A predicate transformer p : ΩY → ΩX is finitary if and only if p is probabilities). Our goal is a healthiness result in this setting, towards which we rely on our relative algebra recipe. As we noted the original The- orem 4.8 is not enough; we use its finitary variant (Theorem 4.19), providing its ingredient (a relative algebra Ω) by means of the lifting result (Proposition 4.12). D It turns out that the category in the relative algebra recipe is given by so-called generalized effect modules. They have been used in the context of categorical quantum logics [19] and the more general theory of effectuses [5]. continuous with respect to the product topology of ΩY and ΩX . Definition 5.3 ( ). A partial commutative monoid (PCM) GEMod ❽ ❽❽ ❽ ❽ ❽ ❽ ❽ is a set M with a partial binary sum and a zero element 0 ∈ M that ' ' '