The Path Algebra of The Endomorphism

Stewart (2026d), *The Endomorphic Collapse as the Foundations of Mathematics*, derives a directed graph Q on four nodes (L, S, T, C) with six directed edges, three independent cycles, and first Betti number three. The four nodes are the four foundations of mathematics logic, set theory, type theory, category theory used in that order. The six edges are the directed operational dependencies between them, with the bilateral equivalences established by Curry and Feys (1958), Howard (1969/1980), Lambek (1972), and Lawvere (1970) as the evidence that the translations exist. This paper constructs the path algebra kQ of that graph, takes the quotient by the binary cycle relations and the convergence constraint at T,…