It is therefore unambiguous to use sets to declare the type of a variable. In mathematics '.' projects a vector into a scalar. The formal meaning of a structure is as a collection of maps. This means that all types with two maps called 1st and 2nd into the A and B respectively, is modeled by Pairs. This means that we can map Pairs into any other type without loosing the information about 1st and 2nd items.
Pairs encodes all sets of objects with two components.
Sets of structures are universal. Codd has shown that any set of data can be expressed as simple structured tables. This justifies modelling all abstract objects as tuples. A collection of sets of tuples is a relational data base and forms a category. The objects in an object oriented design also forms a similar category.