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Twist and ribbon structure
Definition
Let be a braided rigid monoidal category with braiding , and fix left duals for all objects together with the dual-morphism operation of The dual of a morphism.
A twist on is a natural automorphism such that
for all objects and .
A ribbon structure is a twist satisfying the dual-compatibility condition
Depends on
Used by
- A braiding alone does not define a link trace Counterexample
- The unnormalized ribbon trace is not an unframed Markov invariant Counterexample
- Modular ribbon fusion category and Hopf-link data Definition
- Pointed ribbon categories from abelian 3-cocycles Definition
- The ribbon evaluation of an X-colored closed braid Definition
- The specified rank-one divided-power tilting category Definition
- Unitary ribbon data Definition
- Writhe normalization cancels a ribbon kink Example
- All-label unitary Ising normal data and ribbon coherence Lemma
- Balancing and the Hopf-link character identity Lemma
- Multicolored ribbon graphs with arbitrary coupons have a unique evaluation Lemma
- The complete Kirby-color band-slide identity with open colored graph coupons Lemma
- The corrected finite rank-one R series gives the full tilting ribbon structure Lemma
- The explicit Fibonacci model has a positive spherical pivotal structure Lemma
- The ribbon trace equals the framed-closure evaluation Lemma
- The scalar twist controls the two Markov stabilizations Lemma
- A ribbon object defines a unique framed-tangle evaluation functor Theorem
- A twist on a braided rigid category is the same thing as a pivotal structure of Drinfeld type Theorem
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Definition 8.10.1 (standard reference, not scraped)