A Classification of Six Functor Formalisms via Structured Spaces

We lay out an infinity categorical interpretation of reconstruction theorems which are germane to the symmetric monoidal perspective of noncommutative algebraic geometry, present sufficient conditions which allow for the factorization of certain six functor formalisms through animated S-stacks, and give a six functor formalism through which the aforementioned six functor formalisms factor through. Furthermore, and what is arguably the main feat of this article, these achievements, though in appearance arising from disparate concerns, are realized in the dissipation of a familiar thematic tension: that between space and quantity.