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Dec 10, 2013 at 17:40 comment added ex0du5 And just a brief more on why the objects of a CCC are types and not "objects" (or instances) in computer science: look at functions. E.g. the "int max(int first, int second)" maximum function is a morphism of types because it can take any instance of int x int and map it to an instance of int. Category theory has a mechanism for identifying logical "elements" through the maps from the terminal object, but we really want to talk more generically. When we compose functions, we aren't composing instances of application, we are creating a new function that operates on all instances.
Dec 10, 2013 at 7:56 history answered ex0du5 CC BY-SA 3.0