November 2017
Intermediate to advanced
670 pages
17h 35m
English
A cartesian closed category, where a product exists for any two elements and an exponential exists for any two elements, is a model for logic and type theory.
Though many categories have products and sums, only a few have map objects. Such categories are called cartesian closed categories.
There is a deep connection between λ-calculus, logic, and cartesian closed categories.
A cartesian closed category (CCC) is an abstraction having a small vocabulary with associated laws:
The category part means we have a notion of morphisms each having a domain and codomain object. There is an identity morphism for and associative composition operator.
The cartesian part means that we have products, with projection functions ...