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Authors: Leung, Poon
Date: 2017
Subject Keyword: tangent structure | weil algebra
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1247970
Description: At the heart of differential geometry is the construction of the tangent bundle of a manifold. There are various abstractions of this construction, and of particular interest here is that of Tangent S ... More
Reviewed: Reviewed
Date: 2017
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1248004
Description: We study the existence and left properness of transferred model structures for “monoid-like” objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for i ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1191544
Description: We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and ho-motopy local presentability. The main resu ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1202828
Description: It was argued by Crans that it is too much to ask that the category of Gray-categories admit a well behaved monoidal biclosed structure. We make this precise by establishing undesirable properties tha ... More
Reviewed: Reviewed
Authors: Kachour, Camell
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/359738
Description: In this paper we define a sequence of monads T(∞, n)(n ε N) on the category ∞-Gr of ∞-graphs. We conjecture that algebras for T(∞, 0), which are defined in a purely algebraic setting, are models of ∞- ... More
Reviewed: Reviewed
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
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
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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.
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Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/327610
Description: The goal of this paper is to demystify the role played by the Reedy category axioms in homotopy theory. With no assumed prerequisites beyond a healthy appetite for category theoretic arguments, we pre ... 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
Authors: Garner, Richard
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/177316
Description: We call a finitely complete category diexact if every difunctional relation admits a pushout which is stable under pullback and itself a pullback. We prove three results relating to diexact categories ... More
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Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/140427
Description: Quantum categories were introduced in [5] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definitio ... More
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Reviewed: Reviewed
Authors: Egger, J. M
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/146807
Description: In this paper, we consider a non-posetal analogue of the notion of involutive quantale [MP92]; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order o ... More
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Reviewed: Reviewed