Making strip folding a monoidal category

Folding a paper strip made up of n congruent squares into the form of a single square is called strip folding. Strip folding has been studied from a computational and an applicational perspective as a subject in flat-folding origami. In this manuscript, we discern the algebraic structure beneath the folding behavior by defining two sorts of operators. We demonstrate how each operator cooperates with the other in a loosely defined "linear" manner. With all of the flatly folded states of the strips serving as its objects and composited operations serving as its morphisms, this algebraic structure also serves as a possible construction of a monoidal category. Our finding suggests the possibility of employing some algebraic methodologies to strip folding. Conversely, strip folding can be used to visualize some abstract categorical concepts.