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Abstract: . In this paper I extend Gray's tensor product of 2-categories to a new tensor product of Gray-categories. I give a description in terms of generators and relations, one of the relations being an "interchange" relation, and a description similar to Gray's description of his tensor product of 2-categories. I show that this tensor product of Gray-categories satisfies a universal property with respect to quasi-functors of two variables, which are defined in terms of lax-natural transformations... (Update)
Context of citations to this paper: More
.... extra requirement of functoriality in both variables at the same time , makes the category of Gray categories into a monoidal category [19], denoted 3D Teisi. For higherdimensional teisi, it should still be possible to make C Omega D into a tas, but the tensor product thus...
...raising. Exactly with the application of defining semistrict 4 categories in mind, I introduced a tensor product for Gray categories [11]. For Gray categories C and D , their tensor product C Omega D has as generators expressions c Omega d of dimension p q for c 2C p...
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On Braidings, Syllepses, and Symmetries - Crans (1998) (Correct)
Localizations of Transfors - Crans (1998) (Correct)
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0.7: Generalized Centers of Braided and Sylleptic Monoidal 2-Categories - Crans (1997) (Correct)
0.6: This is a collation of the operative parts of a proposal.. - Categories And Related (Correct)
0.6: Project Description: - Higher Categorical Structures (Correct)
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BibTeX entry: (Update)
S. E. Crans, A tensor product for Gray-categories, Preprint 97/222, Macquarie University. http://citeseer.ist.psu.edu/crans99tensor.html More
@misc{ crans-tensor,
author = "S. Crans",
title = "A tensor product for Gray-categories",
text = "S. E. Crans, A tensor product for Gray-categories, Preprint 97/222, Macquarie
University.",
url = "citeseer.ist.psu.edu/crans99tensor.html" }
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10 Algebraic homotopy types (context) - Joyal, Tierney
9 Coherence for bicategories and indexed categories (context) - Lane, Par'e - 1985
9 Algebraic models of 3-types and automorphism structures for .. (context) - Brown, Gilbert - 1989
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8 The role of Michael Batanin's monoidal globular categories - Street
8 A general coherence result (context) - Power - 1989
7 Braided monoidal 2-categories (context) - Baez, Neuchl et al. - 1996
5 a talk about cubes, pasting schemes and teisi, talk at the A.. (context) - Crans, ng - 1995
4 Formal category theory: adjointness in 2-categories (context) - Gray - 1974
3 Topological Quantum Field Theories (context) - Crane, Yetter et al.
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Documents on the same site (http://www.math.mcgill.ca/~crans/papers/): More
Pasting Schemes for the Monoidal Biclosed Structure on - Crans (1995) (Correct)
Localizations of Transfors - Crans (1998) (Correct)
Generalized Centers of Braided and Sylleptic Monoidal 2-Categories - Crans (1997) (Correct)
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