# nLab Crane-Yetter model

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## Surveys, textbooks and lecture notes

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• Axiomatizations

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• Tools

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• Structural phenomena

• Types of quantum field thories

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# Contents

## Idea

The Crane-Yetter model is a 4d TQFT, not to be confused with the Yetter model.

It was defined originally as a state sum in State-Sum Invariants of 4-Manifolds. One labels the elements of a triangulation with objects and morphisms of a ribbon fusion category, usually the representation category of a quasitriangular Hopf algebra, or quantum group.

(The Yetter model, on the contrary, is defined for a finite 2-group.)

## Relation to Turaev-Viro model on the boundary

The 3d TQFT Turaev-Viro model is a boundary field theory of the Crane-Yetter model (Barrett&Garcia-Islas&Martins 04, theorem 2).

### As a fully extended TQFT

It can be understood as an extended topological quantum field theory, see 4-3-2 8-7-6.

## Relation to BF-theory and Dijkgraaf-Witten theory

It is expected that the classical limit of the Crane-Yetter TQFT is BF theory. See John Baez’s article. A state sum model like the Crane-Yetter model, but with a classical Lie group, would be the Ooguri model?. We could understand the Crane-Yetter as a Dijkgraaf-Witten theory with a quantum group instead of a classical group, whereas the Yetter model is a Dijkgraaf-Witten theory with a 2-group. See also this blog post.

Last revised on November 18, 2014 at 23:34:32. See the history of this page for a list of all contributions to it.