Category of Δ-functors
We define the category FuncΔ with functors F:DF→ Scott (DFεCPO) as objects and pairs \((f:D_F \to D_G ,\eta :F\mathop \to \limits^ \cdot G \circ f)\) as morphisms (η is a natural transformation). We show that this category is closed under the common domain theoretical operations +,X,⊥ and →. The category FuncΔ is an O-category and all the operations we define on it are continuous functors, so we will be able to solve recursive equations in FuncΔ. We also show that if we restrict FuncΔ to functors that preserve directed colimits then the category is not closed under the → operation. The category FuncΔ is a basis for a model of second-order lambda calculus with subtyping.
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