In category theory, a branch of mathematics, duality is a correspondence between the properties of a category "C" and the dual properties of the opposite category "C"op. 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 "C"op. 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 "C"op. Also, if a statement is false about "C", then its dual has to be false about "C"op.