Macquarie University, Sydney Macquarie University ResearchOnline

Showing items 1 - 15 of 35.

Add to Quick Collection   All 35 Results

Sort:
 Add All Items to Quick Collection
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1046831
Description: Algebraic weak factorisation systems (awfs) refine weak factorisation systems by requiring that the assignations sending a map to its first and second factors should underlie an interacting comonad–mo ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1046843
Description: We investigate the categories of weak maps associated to an algebraic weak factorisation system (awfs) in the sense of Grandis–Tholen [14]. For any awfs on a category with an initial object, cofibrant ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1191537
Description: We describe a general framework for notions of commutativity based on enriched category theory. We extend Eilenberg and Kelly's tensor product for categories enriched over a symmetric monoidal base to ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1047397
Description: This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory-categorifying the classical theory of categories enriched in a monoidal category-up ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1191455
Description: We provide direct inductive constructions of the orientals and the cubes, exhibiting them as the iterated cones, respectively, the iterated cylinders, of the terminal strict globular ω-category.
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1200772
Description: Among monoidal categories with finite coproducts preserved by tensoring on the left, we characterise those with finite biproducts as being precisely those in which the initial object and the coproduct ... More
Reviewed: Reviewed
Authors: Garner, Richard
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/361622
Description: We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of generalised algebraic theories in the sense of Cartmell, and e ... More
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
Authors: Garner, Richard
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/361637
Description: In 1966, John Isbell introduced a construction on categories which he termed the "couple category" but which has since come to be known as the Isbell envelope. The Isbell envelope, which combines the ... More
Reviewed: Reviewed
Authors: Garner, Richard
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/327637
Description: We provide a diagrammatic criterion for the existence of an absolute colimit in the context of enriched category theory.
Full Text: Full Text
Reviewed: Reviewed
Authors: Garner, Richard
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/328483
Description: We consider the equivalence of Lawvere theories and finitary monads on Set from the perspective of F-enriched category theory, where F is the monoidal category of finitary endofunctors of Set under co ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332223
Description: Restriction categories were introduced as a simple equational axiomatisation for categories of partial maps such as those which arise in the foundations of computability theory. A restriction structur ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332112
Description: We show that Hofmann's and Curien's interpretations of Martin-Löf's type theory, which were both designed to cure a mismatch between syntax and semantics in Seely's original interpretation in locally ... More
Reviewed: Reviewed
Authors: Garner, Richard
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/327621
Description: 16 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/328495
Description: We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a func ... More
Reviewed: Reviewed