In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial assignments of concurrent/distributed computing architectures and associated binary codes to networks and their subsystems, a categorical form of the Hopfield network dynamics, which recovers the usual Hopfield equations when applied to a suitable category of weighted codes, a functorial assignment to networks of corresponding information structures and information cohomology, and a cohomological version of integrated information.

翻译：本文发展了一种新颖的数学形式体系，用于建模具有附加结构的神经信息网络，这些结构以计算资源、代谢资源或信息资源的分配形式存在。该构造的起点是同伦论中的求和函子概念及Segal的Gamma空间概念。本文的主要结果包括：对网络及其子系统进行函子性分配，得到并发/分布式计算架构及相关的二进制编码；提出Hopfield网络动力学的范畴化形式，当应用于适当的加权编码范畴时可恢复通常的Hopfield方程；建立网络到相应信息结构及信息上同调的函子性对应；以及提出整合信息的上同调版本。