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Authors: Street, Ross
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/215107
Description: Spurred by the new examples found by Kornel Szlachányi of a form of lax monoidal category, the author felt the time ripe to publish a reworking of Eilenberg and Kelly's original paper on closed catego ... 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
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/161708
Description: We show that some recent constructions in the literature, named ‘weak’ generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Cartesian monoidal cate ... More
Reviewed: Reviewed
Authors: Street, Ross
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/205123
Description: This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explai ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/191110
Description: 18 page(s)
Full Text: Full Text
Reviewed: Reviewed
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
Full Text: Full Text
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/164682
Description: The aim is the proof of the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product grou ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/161737
Description: Monoidal objects (or pseudomonoids) in monoidal bicategories share many of the properties of the paradigmatic example: monoidal categories. The existence of (say, left) duals in a monoidal category le ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/160281
Description: A weak mixed distributive law (also called weak entwining structure [8]) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generalizes a mixed dist ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/135776
Description: This paper presents non-commutative and structural notions of torsor. The two are related by the machinery of Tannaka-Krein duality.
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/140201
Description: We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg-Moore category MT is monoidal and the forgetful functor MT→M is separable Frobenius. Whenever M is a ... More
Reviewed: Reviewed
Authors: Street, Ross
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/90995
Description: Much Australian work on categories is part of, or relevant to, the development of higher categories and their theory. In this note, I hope to describe some of the origins and achievements of our effor ... More
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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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: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/190226
Description: Separable Frobenius monoidal functors were defined and studied under that name by Szlachanyi and by Day and Pastro, and in a more general context by Cockett and Seely. Our purpose here is to develop t ... More
Reviewed: Reviewed