Institut de Mathématiques de Luminy

Abstract 2002-23

Ruet Paul.
Self-adjoint negation.

If X is a cartesian closed category with an initial object, the following three conditions are equivalent: (1) involutiveness of the negation functor : up to isomorphism, (2) self-adjointness of — , (3) existence of a natural transformation from — to idX . This strengthens a result of Joyal saying that condition (1) makes X a preorder.


Last update : june 6, 2003, EL.