Macquarie University, Sydney Macquarie University ResearchOnline

Showing items 1 - 12 of 12.

Add to Quick Collection   All 12 Results

  • First
  • Previous
  • 1
  • Next
  • Last
Sort:
 Add All Items to Quick Collection
Authors: Weber, Mark
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1053068
Description: Inspired by recent work of Batanin and Berger on the homotopy theory of operads, a general monad-theoretic context for speaking about structures within struc- tures is presented, and the problem of co ... More
Reviewed: Reviewed
Authors: Weber, Mark
Date: 2015
Subject Keyword: perads | polynomial functors
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1053062
Description: In this article we give a construction of a polynomial 2-monad from an operad and describe the algebras of the 2-monads which then arise. This construction is different from the standard construction ... More
Reviewed: Reviewed
Authors: Weber, Mark
Date: 2015
Subject Keyword: polynomial functors | 2-monads
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/361695
Description: The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category ε, is generalised for ε just having pullbacks. The 2-categorical analogue of the theory of polynomials ... More
Reviewed: Reviewed
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
Full Text: Full Text
Reviewed: Reviewed
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: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173355
Description: After a review of the concept of "monad with arities" we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/165771
Description: One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globu ... More
Reviewed: Reviewed
Authors: Weber, Mark
Date: 2007
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/138736
Description: We define and study familial 2-functors primarily with a view to the development of the 2-categorical approach to operads of [Weber, 2005]. Also included in this paper is a result in which the well-kn ... More
Reviewed: Reviewed
Authors: Weber, Mark
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/70200
Description: A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the Yoneda structure (Street and Walters, J. Algebra, 50:350–379, 1978) it generates are exp ... More
Reviewed: Reviewed
Authors: Weber, Mark
Date: 2005
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1130517
Description: 32 page(s)
Reviewed: Reviewed
Authors: Weber, Mark
Date: 2004
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1095857
Description: Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined ... More
Reviewed: Reviewed
  • First
  • Previous
  • 1
  • Next
  • Last