Continuous Functions on Final Comodels of Free Algebraic Theories

11/21/2022

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by   Tomoya Yoshida, et al.

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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.