Network Sheaves Valued in Categories of Adjunctions and their Laplacians



We report past and ongoing efforts to compute (global) sections of cellular sheaves valued in categories of adjunctions. First, we discuss previous work on sheaves valued in the category of complete lattices and Galois connections. Then, we survey ongoing efforts to generalize the fixed point theorem (Theorem 1) to (i) the category of (sufficiently small) categories and adjunctions, and (ii) the category of ordered monoid -enriched categories and adjunctions.