In
category theory, a branch of
mathematics,
duality is a correspondence between properties of a category
C and so-called
dual properties of the
opposite category Cop. Given a statement regarding the category
C, by interchanging the
source and
target of each
morphism as well as interchanging the order of
composing two morphisms, a corresponding dual statement is obtained regarding the opposite category
Cop.
Duality, as such, is the assertion that truth is invariant under this operation on statements. In other words, if a statement is true about
C, then its dual statement is true about
Cop. Also, if a statement is false about
C, then its dual has to be false about
Cop.