By Kamps K.H., Porter T.
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A 3-type is representable by a (G2 , ⊗)-groupoid as we have noted and the category of 2types ‘is’ the ‘category’ of 2-groupoids. An action of a 3-type on a 2-type can thus be studied via (G2 , ⊗)-functors (or lax-versions of them) from a 3-type model to the (G2 , ⊗)-category of 2-groupoids itself. (Grothendieck viewed his programme as part of a higher dimensionl Galois theory. ) 4. Conclusion We have tried to indicate some of the ways in which (G2 , ⊗)-categories arise in algebra and topology, both as large examples such as Top and Ch and small ones modelling homotopy 3-types or as braided monoidal categories that might arise as categories of representations.
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2-Groupoid Enrichments in Homotopy Theory and Algebra by Kamps K.H., Porter T.