A left (resp. right) autonomous category is a monoidal category where every object has a left (resp. right) dual. An autonomous category is a monoidal category where every object has both a left and a right dual. Rigid category is a synonym for autonomous category.
The concepts of *-autonomous category and autonomous category are directly related, specifically, every autonomous category is *-autonomous. A *-autonomous category may be described as a linearly distributive category with (left and right) negations; such categories have two monoidal products linked with a sort of distributive law. In the case where the two monoidal products coincide and the distributivities are taken from the associativity isomorphism of the single monoidal structure, one obtains autonomous categories.
Notes and references
- Yetter, David N. (2001). Functorial Knot Theory. World Scientific. ISBN 981-02-4443-6.
- Berman, Stephen; Yuly Billi (2003). Vertex Operator Algebras in Mathematics and Physics. American Mathematical Society. ISBN 0-8218-2856-8.
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