Geodesic
Spheres as Frobenius objects
Theory and applications of categories, Tome 33 (2018), pp. 691-726

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Following the pattern of the Frobenius structure usually assigned to the 1-dimensional sphere, we investigate the Frobenius structures of spheres in all other dimensions. Starting from dimension d=1, all the spheres are commutative Frobenius objects in categories whose arrows are (d+1)-dimensional cobordisms. With respect to the language of Frobenius objects, there is no distinction between these spheres - they are all free of additional equations formulated in this language. The corresponding structure makes out of the 0-dimensional sphere not a commutative but a symmetric Frobenius object. This sphere is mapped to a matrix Frobenius algebra by a 1-dimensional topological quantum field theory, which corresponds to the representation of a class of diagrammatic algebras given by Richard Brauer.

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Classification : 18D35, 57R56
Keywords: symmetric monoidal category, commutative Frobenius object, oriented manifold, cobordism, normal form, coherence, topological quantum field theory, Brauerian representation 
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     author = {Djordje Baralic and Zoran Petric and Sonja Telebakovic},
     title = {Spheres as {Frobenius} objects},
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Djordje Baralic; Zoran Petric; Sonja Telebakovic. Spheres as Frobenius objects. Theory and applications of categories, Tome 33 (2018), pp. 691-726. http://geodesic.mathdoc.fr/item/TAC_2018_33_a23/