Baez, John C.; Langford, Laurel 2-tangles. (English) Zbl 0905.57017 Lett. Math. Phys. 43, No. 2, 187-197 (1998). In the note under review, by semistrict braided monoidal \(2\)-categories are meant those defined by J. C. Baez and M. Neuchl [Adv. Math. 121, No. 2, 196-244 (1996; Zbl 0855.18008)], but satisfying certain extra axioms introduced by S. Crans [Generalized centers of braided and sylleptic monoidal \(2\)-categories. To appear in Adv. Math.]. The note is in fact an announcement of a theorem claiming that the \(2\)-category of unframed unoriented \(2\)-tangles in four dimensions can be characterized as the “free semistrict braided monoidal \(2\)-category with duals on one unframed self-dual object”. A proof using the movie moves of Carter, Rieger, and Saito is promised to be given in a forthcoming paper. The authors have hopes that there are interesting examples of semistrict braided monoidal \(2\)-categories. They comment on how the above mentioned characterization might be used to construct invariants of \(2\)-tangles in four dimensions. Reviewer: J.Korbaš (Bratislava) Cited in 8 Documents MSC: 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010) 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 57R40 Embeddings in differential topology Keywords:\(2\)-tangle; surface; manifold; smooth embedding in Euclidean space; semistrict braided monoidal \(2\)-category; unframed self-dual object; movie moves Citations:Zbl 0855.18008 PDFBibTeX XMLCite \textit{J. C. Baez} and \textit{L. Langford}, Lett. Math. Phys. 43, No. 2, 187--197 (1998; Zbl 0905.57017) Full Text: DOI arXiv