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用树类形式展示了溪流处理器$A ⁇ mathbb{N ⁇ \\rightrow B ⁇ mathb{N ⁇ $。2021年,Garner以代数理论和共同模型的形式展示了这一表述方式:无限溪流的集合$A ⁇ mathbb{N ⁇ $是以美元计值的投入值$mathbb{T ⁇ A$的代数理论的最后共同模型,而溪流处理器的组合$mathbb{N ⁇,B ⁇ mathb{N ⁇ ]$可以被视为最终的 $mathbb{T ⁇ A$-$\mathbb{T ⁇ B$B$B$B$B_bimodel。在本文中,我们概括了加纳对免费河流理论的研究结果。
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