Adjoint exactness

Abstract

Plato's ideas and Aristotle's real types from the classical age, Nominalism and Realism of the mediaeval period and Whitehead's modern view of the world as pro- cess all come together in the formal representation by category theory of exactness in adjointness (a). Concepts of exactness and co-exactness arise naturally from ad- jointness and are needed in current global problems of science. If a right co-exact valued left-adjoint functor ( ) in a cartesian closed category has a right-adjoint left- exact functor ( ), then physical stability is satis ed if itself is also a right co-exact left-adjoint functor for the right-adjoint left exact functor ( ): a a . These concepts are discussed here with examples in nuclear fusion, in database interroga- tion and in the cosmological ne structure constant by the Frederick construction