nLab
ribbon category

Skip the Navigation Links | Home Page | All Pages | Recently Revised | Authors | Feeds | Export |

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

  • trace

  • traced monoidal category?

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Examples

Theorems

In higher category theory

Edit this sidebar

Definition

A ribbon category (also called a tortile category) is a braided pivotal category, or equivalently a balanced autonomous category, which satisfies θ *=θ, where θ is the twist. This is a kind of category with duals.

Revised on June 2, 2010 21:35:21 by Mike Shulman (128.135.72.152)
Edit | Back in time (3 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: Timeline of category theory and related mathematics, Day convolution, monoidal category, tensor product, symmetric monoidal category, braided monoidal category, multicategory, periodic table, cartesian monoidal category, k-tuply monoidal n-category, cartesian closed category, locally cartesian closed category, Crans-Gray tensor product, monoidal model category, pushout-product axiom, closed monoidal category, strict monoidal category, dagger-compact category, trace, dualizable object, string diagram, compact closed category, k-tuply monoidal (n,r)-category, star-autonomous category, closed monoidal structure on presheaves, exponential object, distributive category, monoidal (infinity,1)-category, symmetric monoidal (infinity,1)-category, fusion category, rigid monoidal category, semisimple category, Oberwolfach Workshop, June 2009 -- Strings, Fields, Topology, modular tensor category, Oberwolfach Workshop, June 2009 -- Abstracts, Oberwolfach Workshop, June 2009 -- Monday, June 8, symmetric monoidal functor, semicartesian monoidal category, cartesian bicategory, braided monoidal 2-category, knot invariant, tensor category, monoidal functor, oplax monoidal functor, internal category in a monoidal category, coherence theorem for monoidal categories, tensor power, monoidal categories - contents, closed functor, monoidal bicategory, pivotal category, bicartesian closed category, finite quantum mechanics in terms of dagger-compact categories, compact double category, symmetric monoidal dagger-category, symmetric algebra, ribbon category, category with duals, twist, bimonoidal category, spherical category, monoid axiom in a monoidal model category, symmetric monoidal (infinity,n)-category, model structure on monoids in a monoidal model category, premonoidal category, cartesian functor, monoidal structure map, cartesian closed (infinity,1)-category, category of monoids, closed monoidal (infinity,1)-category, braided monoidal functor, Hopf adjunction, evaluation map, Frobenius monoidal functor, bilax monoidal functor, monoidal Quillen adjunction, commutative monoid in a symmetric monoidal (infinity,1)-category, fully dualizable object, (infinity,n)-category with duals, Spanier-Whitehead duality, monoidal derivator, Picard group, contents of contents, Mac Lane's proof of the coherence theorem for monoidal categories, Picard 3-group, cartesian closed functor, Deligne tensor product of abelian categories, symmetric multicategory, coherence theorem for symmetric monoidal categories, permutative category, bipermutative category, tensor product of modules, internal hom of chain complexes, tensr product of chain complexes, tensor product of chain complexes, tensor product of abelian groups, coherence theorem for braided monoidal categories, coherence theorem for monoidal bicategories, coherence theorem for braided monoidal bicategories, coherence theorem for symmetric monoidal bicategories, sylleptic monoidal 2-category, braided geometry, Picard 2-group, Picard infinity-group, cartesian monoidal (infinity,1)-category, monoidal (2,1)-category, Drinfeld center