Towards a Complex Variable Interpretation of Peirce’s Existential Graphs

monoid can be defined. Monoidal categories are ubiquitous: cartesian categories (in particular, the category of sets), free word-category over any category, endofunctors category over any category, category of R-modules over a commutative ring R, etc. The abstract monoids definable in the monoidal category incarnate in the usual monoids, triples (or monads), R-algebras, etc. 2 Given a monoidal category C with tensor product ⊗, and given a contravariant functor F:C→C, a force for F is a natural transformation θab : F(a)⊗ b → F(a⊗ b). The forces, introduced by Max Kelly in the 1980’s to solve difficult coherence problems (reduction of the commutativity of an infinity of diagrams to the commutativity of finite of them), have emerged afterwards in domains farther apart: curvatures in grassmannians, sub-riemannian geometry, weak forces in subatomic physics, counting operators in linear logic, etc. Here, the forces appear in another unexpected context: intuionistic logic and existential graphs.