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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1191399
Description: As left adjoint to the dual algebra functor, Sweedler’s finite dual construction is an important tool in the theory of Hopf algebras over a field. We show in this note that the left adjoint to the dua ... More
Reviewed: Reviewed
Authors: Street, Ross
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195342
Description: Motivated by the weighted Hurwitz product on sequences in an algebra, we produce a family of monoidal structures on the category of Joyal species. We suggest a family of tensor products for charades. ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/360537
Description: We prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let X denote an additive category with finit ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/355915
Description: This paper extends the Day Reflection Theorem to skew monoidal categories. We also provide conditions under which a skew monoidal structure can be lifted to the category of Eilenberg-Moore algebras fo ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/353005
Description: The Catalan numbers are well known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/325513
Description: A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are sp ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/325562
Description: 2 page(s)
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/341196
Description: Foreword of Special Issue in Honour of Professor George Janelidze, on the occasion of his 60th birthday. Proceedings of the "Workshop on Category Theory, an international conference at the Universidad ... More
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/339903
Description: We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoid ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/305754
Description: A concrete model of the free skew-monoidal category Fsk on a single generating object is obtained. The situation is clubbable in the sense of G.M. Kelly, so this allows a description of the free skew- ... More
Reviewed: Reviewed
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
Authors: Street, Ross
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/189652
Description: The Tamari lattice provides an example of a (non-symmetric) operad. We discuss such operads and their associated monads and monoidal categories. Freeness is an important aspect. The free structures ar ... More
Reviewed: Reviewed