Structs are an example of a "universal construction" called a product. Other examples of this include cartesian products, logical AND and join in a lattice (e.g

Structs are an example of a "universal construction" called a product. Other examples of this include cartesian products, logical AND and join in a lattice (e.g. getting the least upper bound of two partially ordered elements). For types, this is defined exclusively based on the functions it has. Roughly speaking, the product of two types A and B is the "simplest" structure that has a function to A and a function to B--that is, if you imagine a nice diagram, there is an arrow from A × B to A and an arrow from A × B to B. For structs, these two functions are just field accesses. The notion of "simplest" here essentially just means that given any other object C with these criteria--that is, a function to A and a function to B--there has to also exist a function C to A × B. I'm skipping some details, but you should get the general gist. The notion of duality just means taking the above diagram and flipping all the arrows. So the co-product of two types A and B is the "simplest" type A + B that has a function from A to A + B and a function from B to A + B. These functions correspond to tagging elements from A or B as appropriate. For logical AND, the dual is logical OR. For getting the least upper bound, the dual is getting the greatest lower bound. And, following that same logic, for structs the dual is tagged unions. I hope that made sense. This is the sort of thing that's much easier to describe interactively with a whiteboard instead of trying to just use ASCII--it practically begs me to draw some diagrams, but my ASCII art is simply not up to par :(.