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Pasting Schemes for the Monoidal Biclosed Structure on ωCat
, 1995
"... Using the theory of pasting presentations, developed in chapter 2, I give a detailed description of the tensor product on ωcategories, which extends Gray's tensor product on 2categories and which is closely related to BrownHiggins's tensor product on ωgroupoids. Immediate consequences ..."
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Using the theory of pasting presentations, developed in chapter 2, I give a detailed description of the tensor product on ωcategories, which extends Gray's tensor product on 2categories and which is closely related to BrownHiggins's tensor product on ωgroupoids. Immediate consequences are a general and uniform definition of higher dimensional lax natural transformations, and a nice and transparent description of the corresponding internal homs. Further consequences will be in the development of a theory for weak ncategories, since both tensor products and lax structures are crucial in this.
Free Products of Higher Operad Algebras
, 909
"... Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, ..."
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Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an noperad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure