Abstract :
MacLaneʹs original introduction to the theory of monoidal categories presented a short argument, due to Isbell, of why the concept of ‘associativity up to isomorphism’ is needed for a reasonable conception of a monoidal tensor. This argument was based on the properties of a distinguished object D in a category with a product, satisfying D=D×D. In the following paper, we demonstrate that a slight modification of this property allows us to construct elements of End(D) that have similar properties to associativity isomorphisms in a monoidal category, and show how these can be used to construct what can reasonably be considered to be a weakening of the associativity of a strict monoidal category.
