We examine a monoidal structure on the category of polynomial functors, defined through the operation of substituting one polynomial into another. We explain how this composition product transforms polynomials into a richer algebraic structure, enabling the modeling of more complex interactions and processes. The chapter explores the properties of this monoidal structure, how it relates to existing constructions in category theory, and its implications for understanding time evolution and dynamical behavior. We also provide examples and visual representations to clarify how substitution works in practice.