1,508 research outputs found
Lifting Coalgebra Modalities and Model Structure to Eilenberg-Moore Categories
A categorical model of the multiplicative and exponential fragments of
intuitionistic linear logic (), known as a \emph{linear
category}, is a symmetric monoidal closed category with a monoidal coalgebra
modality (also known as a linear exponential comonad). Inspired by Blute and
Scott's work on categories of modules of Hopf algebras as models of linear
logic, we study categories of algebras of monads (also known as Eilenberg-Moore
categories) as models of . We define a lifting
monad on a linear category as a Hopf monad -- in the Brugui{\`e}res, Lack, and
Virelizier sense -- with a special kind of mixed distributive law over the
monoidal coalgebra modality. As our main result, we show that the linear
category structure lifts to the category of algebras of lifting
monads. We explain how groups in the category of coalgebras of the monoidal
coalgebra modality induce lifting monads and provide a source
for such groups from enrichment over abelian groups. Along the way we also
define mixed distributive laws of symmetric comonoidal monads over symmetric
monoidal comonads and lifting differential category structure.Comment: An extend abstract version of this paper appears in the conference
proceedings of the 3rd International Conference on Formal Structures for
Computation and Deduction (FSCD 2018), under the title "Lifting Coalgebra
Modalities and Model Structure to Eilenberg-Moore Categories
Evolution of the X-ray Profiles of Poor Clusters from the XMM-LSS Survey
A sample consisting of 27 X-ray selected galaxy clusters from the XMM-LSS
survey is used to study the evolution in the X-ray surface brightness profiles
of the hot intracluster plasma. These systems are mostly groups and poor
clusters, with temperatures 0.6-4.8 keV, spanning the redshift range 0.05 to
1.05. Comparing the profiles with a standard beta-model motivated by studies of
low redshift groups, we find 54% of our systems to possess a central excess,
which we identify with a cuspy cool core. Fitting beta-model profiles, allowing
for blurring by the XMM point spread function, we investigate trends with both
temperature and redshift in the outer slope (beta) of the X-ray surface
brightness, and in the incidence of cuspy cores. Fits to individual cluster
profiles and to profiles stacked in bands of redshift and temperature indicate
that the incidence of cuspy cores does not decline at high redshifts, as has
been reported in rich clusters. Rather such cores become more prominent with
increasing redshift. Beta shows a positive correlation with both redshift and
temperature. Given the beta-T trend seen in local systems, we assume that
temperature is the primary driver for this trend. Our results then demonstrate
that this correlation is still present at z~0.3, where most of our clusters
reside.Comment: Accepted for publication in MNRAS. 15 pages, 12 figure
Covariance matrices for halo number counts and correlation functions
We study the mean number counts and two-point correlation functions, along
with their covariance matrices, of cosmological surveys such as for clusters.
In particular, we consider correlation functions averaged over finite redshift
intervals, which are well suited to cluster surveys or populations of rare
objects, where one needs to integrate over nonzero redshift bins to accumulate
enough statistics. We develop an analytical formalism to obtain explicit
expressions of all contributions to these means and covariance matrices, taking
into account both shot-noise and sample-variance effects. We compute low-order
as well as high-order (including non-Gaussian) terms. We derive expressions for
the number counts per redshift bins both for the general case and for the small
window approximation. We estimate the range of validity of Limber's
approximation and the amount of correlation between different redshift bins. We
also obtain explicit expressions for the integrated 3D correlation function and
the 2D angular correlation. We compare the relative importance of shot-noise
and sample-variance contributions, and of low-order and high-order terms. We
check the validity of our analytical results through a comparison with the
Horizon full-sky numerical simulations, and we obtain forecasts for several
future cluster surveys.Comment: 37 page
Le Progres (Windsor) 1901
Online Holdings
1901: May 23 (Vol. 20: no. 21)https://scholar.uwindsor.ca/progreswindsor/1004/thumbnail.jp
Tangent Categories from the Coalgebras of Differential Categories
Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key example arises from the opposite of the category of Abelian groups with the free exponential modality. The coEilenberg-Moore category, in this case, is the opposite of the category of commutative rings. That the latter is a tangent category captures a fundamental aspect of both algebraic geometry and Synthetic Differential Geometry. The general result applies when there are no negatives and thus encompasses examples arising from combinatorics and computer science
Cartesian Differential Kleisli Categories
Cartesian differential categories come equipped with a differential
combinator which axiomatizes the fundamental properties of the total derivative
from differential calculus. The objective of this paper is to understand when
the Kleisli category of a monad is a Cartesian differential category. We
introduce Cartesian differential monads, which are monads whose Kleisli
category is a Cartesian differential category by way of lifting the
differential combinator from the base category. Examples of Cartesian
differential monads include tangent bundle monads and reader monads. We give a
precise characterization of Cartesian differential categories which are Kleisli
categories of Cartesian differential monads using abstract Kleisli categories.
We also show that the Eilenberg-Moore category of a Cartesian differential
monad is a tangent category.Comment: For the proceedings of MFPS202
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