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

翻译：2009年，Ghani、Hancock和Pattinson给出了流处理器$A^{\mathbb{N}} \rightarrow B^{\mathbb{N}}$的一种树状表示。2021年，Garner表明该表示可通过代数理论和余模型建立：无限流$A^{\mathbb{N}}$的集合是$A$值输入代数理论$\mathbb{T}_A$的最终余模型，而流处理器$\mathit{Top}(A^{\mathbb{N}},B^{\mathbb{N}})$的集合可视为最终$\mathbb{T}_A$-$\mathbb{T}_B$-双模型。本文中，我们将Garner的结果推广至自由代数理论的情形。