A new class of mathematical models for the structure and evolution of information over social networks is proposed, inspired by ideas from algebraic topology. These models have the advantage of being strongly heterogeneous, including differentiating between individuals' internal states and their pairwise external expressions thereof. As well, these models admit a variety of data types as target representations: vector valued, lattice-valued, and more, all possessing a common framework. Finally, these models admit universal notions of diffusion and harmonic state distributions.

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