nLab
category with duals

**monoidal categories** ## With symmetry * braided monoidal category * balanced monoidal category * twist * symmetric monoidal category ## With duals for objects * category with duals (list of them) * dualizable object (what they have) * rigid monoidal category, a.k.a. autonomous category * pivotal category * spherical category * ribbon category, a.k.a. tortile category * compact closed category ## With duals for morphisms * monoidal dagger-category? * symmetric monoidal dagger-category * dagger compact category ## With traces * trace * traced monoidal category ## Closed structure * closed monoidal category * cartesian closed category * closed category * star-autonomous category ## Special sorts of products * cartesian monoidal category * semicartesian monoidal category * multicategory ## Semisimplicity * semisimple category * fusion category * modular tensor category ## Morphisms * monoidal functor (lax, oplax, strong bilax, Frobenius) * braided monoidal functor * symmetric monoidal functor ## Internal monoids * monoid in a monoidal category * commutative monoid in a symmetric monoidal category * module over a monoid ## Examples * tensor product * closed monoidal structure on presheaves * Day convolution ## Theorems * coherence theorem for monoidal categories * monoidal Dold-Kan correspondence ## In higher category theory * monoidal 2-category * braided monoidal 2-category * monoidal bicategory * cartesian bicategory * k-tuply monoidal n-category * little cubes operad * monoidal (∞,1)-category * symmetric monoidal (∞,1)-category * compact double category

Edit this sidebar

Categories with duals

Idea

A category with duals is a category where objects and/or morphisms have duals. This exists in several flavours; this list is mostly taken from a recent categories list post from Peter Selinger.

Categories with duals for objects

Categories with duals for morphisms

One might write something about these too, or put them on a separate page. In the meantime, see the table of contents to the right.

References

Revised on August 21, 2012 10:56:53 by Toby Bartels (98.19.40.130)