Continuous Functions on Final Comodels of Free Algebraic Theories

Abstract

In 2009, Ghani, Hancock and Pattinson gave a tree-like representation of stream processors A[N] → B[N]. In 2021, Garner showed that this representation can be established in terms of algebraic theory and comodels: the set of infinite streams A[N] is the final comodel of the algebraic theory of A-valued input [T][A] and the set of stream processors Top(A[N] , B[N]) can be seen as the final [T][A]-[T][B]-bimodel. In this paper, we generalize Garner's results to the case of free algebraic theories.