Rigid Category (Paperback)

High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, a rigid category is a monoidal category where every object is rigid, that is, has a dual X* (the internal Hom [X, 1]) and a morphism 1 X X* satisfying natural conditions. The category is called right rigid or left rigid according to whether it has right duals or left duals. They were first defined by Dold and Puppe in 1978.An inverse is an object X-1 such that both X X-1 and X-1 X are isomorphic to 1, the one object of the monoidal category. If an object X has a left (resp. right) inverse X-1 with respect to the tensor product then it is left (resp. right) rigid, and X* = X-1. This means every autonomous category is rigid.