925 research outputs found
Introduction to the language of stacks and gerbes
This is an introduction to gerbes for topologists, with emphasis on
non-abelian cohomology.Comment: 30 page
Orbifolds as Groupoids: an Introduction
This is a survey paper based on my talk at the Workshop on Orbifolds and
String Theory, the goal of which was to explain the role of groupoids and their
classifying spaces as a foundation for the theory of orbifolds
A definability theorem for first order logic
For any first order theory T we construct a Boolean valued model M, in which
precisely the T--provable formulas hold, and in which every (Boolean valued)
subset which is invariant under all automorphisms of M is definable by a first
order formula. Our presentation is entirely selfcontained, and only requires
familiarity with the most elementary properties of model theory
On the derived category of an algebra over an operad
We present a general construction of the derived category of an algebra over
an operad and establish its invariance properties. A central role is played by
the enveloping operad of an algebra over an operad.Comment: References and remark 2.5 adde
Topological Representation of Geometric Theories
Using Butz and Moerdijk's topological groupoid representation of a topos with
enough points, a `syntax-semantics' duality for geometric theories is
constructed. The emphasis is on a logical presentation, starting with a
description of the semantical topological groupoid of models and isomorphisms
of a theory and a direct proof that this groupoid represents its classifying
topos. Using this representation, a contravariant adjunction is constructed
between theories and topological groupoids. The restriction of this adjunction
yields a contravariant equivalence between theories with enough models and
semantical groupoids. Technically a variant of the syntax-semantics duality
constructed in [Awodey and Forssell, arXiv:1008.3145v1] for first-order logic,
the construction here works for arbitrary geometric theories and uses a slice
construction on the side of groupoids---reflecting the use of `indexed' models
in the representation theorem---which in several respects simplifies the
construction and allows for an intrinsic characterization of the semantic side.Comment: 32 pages. This is the first pre-print version, the final revised
version can be found at
http://onlinelibrary.wiley.com/doi/10.1002/malq.201100080/abstract (posting
of which is not allowed by Wiley). Changes in v2: updated comment
Axiomatic homotopy theory for operads
We give sufficient conditions for the existence of a model structure on
operads in an arbitrary symmetric monoidal model category. General invariance
properties for homotopy algebras over operads are deduced.Comment: 29 pages, revised for publicatio
A note on the global structure of proper Lie groupoids in low codimensions
We observe that any connected proper Lie groupoid whose orbits have
codimension at most two admits a globally effective representation on a smooth
vector bundle, i.e., one whose kernel consists only of ineffective arrows. As
an application, we deduce that any such groupoid can up to Morita equivalence
be presented as an extension of some action groupoid G n X with G compact by
some bundle of compact Lie groups.Comment: 12 page
- …