Definition
A symmetric monoidal category is compact closed if every object has a dual object. If this holds, the dual object is unique up to canonical isomorphism, and it is denoted .
In a bit more detail, an object is called the dual of A if it is equipped with two morphisms called the unit and the counit, satisfying the equations
and
- .
For clarity, we rewrite the above compositions diagramatically:
and
Read more about this topic: Compact Closed Category
Famous quotes containing the word definition:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)