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Authors: Weber, Mark
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/270105
Description: One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developm ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/269953
Description: In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first principal result - the li ... More
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Authors: Weber, Mark
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/270111
Description: In this paper we unify the developments of [Batanin, 1998], [Batanin- Weber, 2011] and [Cheng, 2011] into a single framework in which the interplay between multitensors on a category V, and monads on ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/270108
Description: Given a horizontal monoid M in a duoidal category ℱ, we examine the relationship between bimonoid structures on M and monoidal structures on the category ℱ*M of right M-modules which lift the vertical ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/186217
Description: A category is adhesive if it has all pullbacks, all pushouts along monomorphisms, and all exactness conditions between pullbacks and pushouts along monomorphisms which hold in a topos. This condition ... More
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Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/191110
Description: 18 page(s)
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Authors: Street, Ross
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/189686
Description: There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocomplet ... More
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Authors: Lack, Stephen
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/139539
Description: Adhesive categories are categories which have pushouts with one leg a monomorphism, all pullbacks, and certain exactness conditions relating these pushouts and pullbacks. We give a new proof of the fa ... More
Reviewed: Reviewed
Authors: Verity, Dominic
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/169993
Description: Originally published as: Ph.D. thesis, Cambridge University, 1992.
Authors: Day, Brian J
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/139584
Description: This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/190014
Description: We generalize to the context internal to an autonomous monoidal bicategory the work of Bruguieres, Virelizier, and the second-named author on lifting closed structure on a monoidal category to the cat ... More
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Authors: Oury, David
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1156700
Description: A combinatorial category Disk was introduced by André Joyal to play a role in his definition of weak ω-category. He defined the category Θ to be dual to Disks. In the ensuing literature, a more concre ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/90348
Description: This is an expanded, revised and corrected version of the first author's 1981 preprint. The discussion of one-dimensional cohomology H¹ in a fairly general category ℇ involves passing to the 2-categor ... More
Reviewed: Reviewed
Date: 2009
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1082801
Description: 20 page(s)
Reviewed: Reviewed
Authors: Street, Ross
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/189996
Description: Distributive laws between monads (triples) were defined by Jon Beck in the 1960s. They were generalized to monads in 2-categories and noticed to be monads in a 2-category of monads. Mixed distributive ... More
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