29 citations · 98 across the 21 of their papers we have counts for
22 papers
On the -topos semantics of homotopy type theory
Emily Riehl
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article…
Rigid models for 2-gerbes I: Chern-Simons geometry
David Michael Roberts, Raymond F. Vozzo
Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is de…
Homotopy types of topological stacks of categories
David Michael Roberts
This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essenti…
Explicit String bundles
David Michael Roberts
While higher bundles are of clear relevance to higher gauge theory, examples other than abelian bundle gerbes are hard to come across. One would in particular like to see 2-bundles…
Substructural fixed-point theorems and the diagonal argument: theme and variations
David Michael Roberts
This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that th…
Many finite-dimensional lifting bundle gerbes are torsion
David Michael Roberts
Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stev…
Topological sectors for heterotic M5-brane charges under Hypothesis H
David Michael Roberts
Assuming Fiorenza-Sati-Schreiber's Hypothesis H, on the charge quantization of M-theory's -field, the topological sectors of the resulting -valued higher gauge…
(Re)constructing Code Loops
Ben Nagy, David Michael Roberts
The Moufang loop named for Richard Parker is a central extension of the extended binary Golay code. It the prototypical example of a general class of nonassociative structures know…
The elementary construction of formal anafunctors
David Michael Roberts
This article gives an elementary and formal 2-categorical construction of a bicategory of right fractions analogous to anafunctors, starting from a 2-category equipped with a famil…
Extending Whitney's extension theorem: nonlinear function spaces
David Michael Roberts, Alexander Schmeding
We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains , with non-smooth boundary, in possibly non-compa…
Quasi-periodic paths and a string 2-group model from the free loop group
Michael Murray, David Michael Roberts, Christoph Wockel
In this paper we address the question of the existence of a model for the string 2-group as a strict Lie-2-group using the free loop group (or more generally for compa…
The smooth Hom-stack of an orbifold
David Michael Roberts, Raymond F. Vozzo
For a compact manifold M and a differentiable stack \cX presented by a Lie groupoid X, we show the Hom-stack Hom(M,\cX) is presented by a Fréchet-Lie groupoid Map(M,X) and so is an…
Smooth loop stacks of differentiable stacks and gerbes
David Michael Roberts, Raymond F. Vozzo
Résumé. Nous définissons un groupoïde de Fréchet-Lie Map(S^1,X) d'ana-foncteurs du cercle vers un groupoïde de Lie X. Ceci fournit une présentation du Hom-champ Hom(S^1,\cX), où \c…
Equivariant bundle gerbes
Michael K. Murray, David Michael Roberts, Danny Stevenson +1
We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes with a view towards studying descent problems and equivariance for bundle gerbes.…
A topological fibrewise fundamental groupoid
David Michael Roberts
It is well-known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. I…
On certain 2-categories admitting localisation by bicategories of fractions
David Michael Roberts
Pronk's theorem on bicategories of fractions is applied, in almost all cases in the literature, to 2-categories of geometrically presentable stacks on a 1-site. We give an proof th…
The weak choice principle WISC may fail in the category of sets
David Michael Roberts
The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of…
A bigroupoid's topology (or, Topologising the homotopy bigroupoid of a space)
David Michael Roberts
The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroup…
The universal simplicial bundle is a simplicial group
David M. Roberts
The classical universal bundle functor W:sGrp(C) \to sSet(C) for simplicial groups in a category C with finite products lifts to a monad on sGrp(C). This result extends to simplici…
Simplicial principal bundles in parametrized spaces
David Michael Roberts, Danny Stevenson
In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we…
On the existence of bibundles
Michael Murray, David Michael Roberts, Danny Stevenson
We consider the existence of bibundles, in other words locally trivial principal spaces with commuting left and right actions. We show that their existence is closely relat…
Internal categories, anafunctors and localisations
David M. Roberts
In this article we review the theory of anafunctors introduced by Makkai and Bartels, and show that given a subcanonical site S, one can form a bicategorical localisation of variou…