4,269 research outputs found
Homotopical Adjoint Lifting Theorem
This paper provides a homotopical version of the adjoint lifting theorem in
category theory, allowing for Quillen equivalences to be lifted from monoidal
model categories to categories of algebras over colored operads. The generality
of our approach allows us to simultaneously answer questions of rectification
and of changing the base model category to a Quillen equivalent one. We work in
the setting of colored operads, and we do not require them to be
-cofibrant. Special cases of our main theorem recover many known
results regarding rectification and change of model category, as well as
numerous new results. In particular, we recover a recent result of
Richter-Shipley about a zig-zag of Quillen equivalences between commutative
-algebra spectra and commutative differential graded
-algebras, but our version involves only three Quillen equivalences
instead of six. We also work out the theory of how to lift Quillen equivalences
to categories of colored operad algebras after a left Bousfield localization.Comment: This is the final, journal versio
Smith Ideals of Operadic Algebras in Monoidal Model Categories
Building upon Hovey's work on Smith ideals for monoids, we develop a homotopy
theory of Smith ideals for general operads in a symmetric monoidal category.
For a sufficiently nice stable monoidal model category and an operad satisfying
a cofibrancy condition, we show that there is a Quillen equivalence between a
model structure on Smith ideals and a model structure on algebra maps induced
by the cokernel and the kernel. For symmetric spectra this applies to the
commutative operad and all Sigma-cofibrant operads. For chain complexes over a
field of characteristic zero and the stable module category, this Quillen
equivalence holds for all operads.Comment: Comments welcom
Arrow Categories of Monoidal Model Categories
We prove that the arrow category of a monoidal model category, equipped with
the pushout product monoidal structure and the projective model structure, is a
monoidal model category. This answers a question posed by Mark Hovey, and has
the important consequence that it allows for the consideration of a monoidal
product in cubical homotopy theory. As illustrations we include numerous
examples of non-cofibrantly generated monoidal model categories, including
chain complexes, small categories, topological spaces, and pro-categories.Comment: 13 pages. Comments welcome. Version 2 adds more examples, and an
application to cubical homotopy theory. Version 3 is the final, journal
version, accepted to Mathematica Scandinavic
Comonadic Coalgebras and Bousfield Localization
For a model category, we prove that taking the category of coalgebras over a
comonad commutes with left Bousfield localization in a suitable sense. Then we
prove a general existence result for left-induced model structure on the
category of coalgebras over a comonad in a left Bousfield localization. Next we
provide several equivalent characterizations of when a left Bousfield
localization preserves coalgebras over a comonad. These results are illustrated
with many applications in chain complexes, (localized) spectra, and the stable
module category
Marginally Trapped Surfaces and AdS/CFT
It has been proposed that the areas of marginally trapped or anti-trapped
surfaces (also known as leaves of holographic screens) may encode some notion
of entropy. To connect this to AdS/CFT, we study the case of marginally trapped
surfaces anchored to an AdS boundary. We establish that such boundary-anchored
leaves lie between the causal and extremal surfaces defined by the anchor and
that they have area bounded below by that of the minimal extremal surface. This
suggests that the area of any leaf represents a coarse-grained von Neumann
entropy for the associated region of the dual CFT. We further demonstrate that
the leading area-divergence of a boundary-anchored marginally trapped surface
agrees with that for the associated extremal surface, though subleading
divergences generally differ. Finally, we generalize an argument of Bousso and
Engelhardt to show that holographic screens with all leaves anchored to the
same boundary set have leaf-areas that increase monotonically along the screen,
and we describe a construction through which this monotonicity can take the
more standard form of requiring entropy to increase with boundary time. This
construction is related to what one might call future causal holographic
information, which in such cases also provides an upper bound on the area of
the associated leaves.Comment: 23 pages, 5 figure
Sharp Fronts Due to Diffusion and Viscoelastic Relaxation in Polymers
A model for sharp fronts in glassy polymers is derived and analyzed. The major effect of a diffusing penetrant on the polymer entanglement network is taken to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms via a relaxation parameter. This accounts for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state due to slow response to changing conditions. Both numerical and analytical perturbation studies of a boundary
value problem for a dry glass polymer exposed to a penetrant solvent are completed. Concentration profiles
in good agreement with observations are obtained
A perturbative perspective on self-supporting wormholes
We describe a class of wormholes that generically become traversable after
incorporating gravitational back-reaction from linear quantum fields satisfying
appropriate (periodic or anti-periodic) boundary conditions around a
non-contractible cycle, but with natural boundary conditions at infinity (i.e.,
without additional boundary interactions). The class includes both
asymptotically flat and asymptotically AdS examples. Simple asymptotically
AdS or asymptotically AdS examples with a single periodic
scalar field are then studied in detail. When the examples admit a smooth
extremal limit, our perturbative analysis indicates the back-reacted wormhole
remains traversable at later and later times as this limit is approached. This
suggests that a fully non-perturbative treatment would find a self-supporting
eternal traversable wormhole. While the general case remains to be analyzed in
detail, the likely relation of the above effect to other known instabilities of
extreme black holes may make the construction of eternal traversable wormholes
more straightforward than previously expected.Comment: Minor corrections (including fixing a factor of 2 in several
formulas/plots
From Dogfight to Teamwork
A squadron of Fokker D-7\u27s is flying along over No-Man\u27s Land; the pilots in their open cockpits are alert, scanning the skies for Allied planes. Suddenly they find them, roaring out of the clouds above. Each Spad picks out a Jerry, breaks formation, and goes after him. From then on it is each man for himself, shooting one plane down and going after another. The only chance for survival lies in out-maneuvering the enemy and letting him have it with the single .30 caliber machine gun. When one side has had enough, it runs for home. This is an aerial battle of World War I
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