nLab Scott-complete category




The notion of Scott-complete categories is a category theoretic generalization of the notion of Scott domains from domain theory, and as such it provides categorical semantics for the un-typed lambda calculus and related programming languages.

A Scott domain is a directed-complete partial order (dcpo) that is

The suitable notion of morphisms between Scott domains is that of directed-join-preserving monotone functions. These are the same as continuous functions with respect to the Scott topology.

Scott domains forms a cartesian closed category that supports the solution of recursive domain equations.

Scott domains admit a simple description in terms of “information systems”, which can help to calculate Scott domains and to cement the computation / information-based intuitions.



A category is Scott-complete if it is

Scott-complete categories and directed colimit-preserving functors form a category SCCSCC.

This category SCCSCC is cartesian closed and supports the solution of recursive domain equations.

See also


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