Macquarie University, Sydney Macquarie University ResearchOnline

Showing items 1 - 15 of 21.

Add to Quick Collection   All 21 Results

Sort:
 Add All Items to Quick Collection
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173503
Description: We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not b ... More
Reviewed: Reviewed
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173388
Description: The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniq ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/177140
Description: 17 page(s)
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
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173349
Description: Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of "exactness" conditions relating the finite limits and the specified colimits. Som ... More
Reviewed: Reviewed
Authors: Lack, Stephen
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173343
Description: Many categorical axioms assert that a particular canonically defined natural transformation between certain functors is invertible. We give two examples of such axioms where the existence of any natur ... 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
Full Text: Full Text
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: Lack, Stephen
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/170463
Description: A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full subcategory Gray-Gpd of ... More
Reviewed: Reviewed
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
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/160272
Description: Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category ... 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/1959.14/140201
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: Lack, Stephen
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/141607
Description: This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory, and ... More
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/351925
Description: Bicategories of spans are characterized as cartesian bicategories in which every comonad has an Eilenberg-Moore object and every left adjoint arrow is comonadic.
Reviewed: Reviewed