nLab
compact closed category

A compact closed category, also called an autonomous monoidal category, is a symmetric monoidal category in which every object is dualizable. If we drop the symmetry requirement, we obtain a rigid monoidal category.

References

The Wikipedia entry isn’t bad:

• Wikipedia, Compact closed category.

Also see section 2.1 in:

• Peter Selinger, Dagger compact closed categories and completely positive maps. pdf