Chapter 27: Mereology: Parts, Wholes, and Composition

Parts compose wholes when colimits exist. Mereological composition is categorical colimit: the whole is the universal construction that receives morphisms from each part compatibly with the part-to-part relations. Restricted composition follows naturally—not everything composes, because not every diagram admits a colimit in the admissible category. The Special Composition Question (“When do parts compose?”) receives a precise structural answer: when the colimit exists. Emergence—genuinely new properties of wholes that are not properties of any part—is demystified: colimits can have properties that none of their coprojection sources possess. This is a structural account of emergence, not a magical one.