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1.
With every subset selection for posets, there is associated a certain ideal completion . As shown by Erné, such completions help to extend classical results on domains and similar structures in the absence of
the required joins. Some results about –predistributive or –precontinuous posets and –continuous functions are summarized and supplemented. In particular, several central results on function spaces in domain
theory are extended to the setting of productive closed subset selections. The category FSBP, in which objects are finitely separated and upper bounded posets and arrows are continuous functions between them, is shown to be cartesian closed.
This research is supported by the National Natural Science Foundation of China, 10471035. 相似文献
2.
A. Gerlo 《Applied Categorical Structures》2008,16(4):479-493
In a topological construct endowed with a proper -factorization system and a concrete functor , we study -compactness and -Hausdorff separation, where is a class of “closed morphisms” in the sense of Clementino et al. (A functional approach to general topology. In: Categorical
Foundations. Encyclopedia of Mathematics and Its Applications, vol. 97, pp. 103–163. Cambridge University Press, Cambridge,
2004), determined by Λ. In particular, we point out under which conditions on Λ, the notion of -compactness of an object of coincides with 0-compactness of the image in Prap. Our results will be illustrated by some examples: except for some well-known ones, like b-compactness of a topological space, we also capture some compactness notions that were not considered before in the literature.
In particular, we obtain a generalization of b-compactness to the setting of approach spaces. This notion is shown to play an important role in the study of uniformizability.
The author is research assistant at the Fund of Scientific Research Vlaanderen (FWO). 相似文献
3.
Applying (enriched) categorical structures we define the notion of ordered sheaf on a quantaloid
, which we call ‘
-order’. This requires a theory of semicategories enriched in the quantaloid
, that admit a suitable Cauchy completion. There is a quantaloid
of
-orders and ideal relations, and a locally ordered category
of
-orders and monotone maps; actually,
. In particular is
, with Ω a locale, the category of ordered objects in the topos of sheaves on Ω. In general
-orders can equivalently be described as Cauchy complete categories enriched in the split-idempotent completion of
. Applied to a locale Ω this generalizes and unifies previous treatments of (ordered) sheaves on Ω in terms of Ω-enriched structures.Mathematics Subject Classifications (2000) 06F07, 18B35, 18D05, 18D20. 相似文献
4.
Valentina Rossi 《Applied Categorical Structures》2006,14(4):291-311
Given a regular Gumm category such that any regular epimorphism is effective for descent, we prove that any Birkhoff subcategory in gives rise to an admissible Galois structure. This result allows one to consider some new applications of the categorical Galois theory in the context of topological algebras. Given a regular Mal’cev category , we first characterize the coverings of the Galois structure induced by the subcategory of the abelian objects in . Then we consider as a subcategory of the category of the equivalence relations in , and we characterize the coverings of the corresponding Galois structure . By composing the Galois structures and we obtain the Galois structure induced by as a subcategory of . We give the characterization of the -coverings in terms of the coverings of and . 相似文献
5.
In this paper we show that each factorization structure on a small category , satisfying certain conditions, yields a presheaf on and a morphism of presheaves . We then give connections, and set up one to one correspondences, between subclasses of the following classes: (a) closure operators on (b) subobjects of (c) morphisms from to (d) weak Lawvere–Tierney topologies (e) weak Grothendieck topologies (f) closure operators on . 相似文献
6.
Ursula Hamenstädt 《Inventiones Mathematicae》2009,175(3):545-609
We construct a geometric model for the mapping class group of a non-exceptional oriented surface S of genus g with k punctures and use it to show that the action of on the compact metrizable Hausdorff space of complete geodesic laminations for S is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of . 相似文献
7.
The semantic constructions and results for definite programs do not extend when dealing with negation. The main problem is
related to a well-known problem in the area of algebraic specification: if we fix a constraint domain as a given model, its
free extension by means of a set of Horn clauses defining a set of new predicates is semicomputable. However, if the language
of the extension is richer than Horn clauses its free extension (if it exists) is not necessarily semicomputable. In this
paper we present a framework that allows us to deal with these problems in a novel way. This framework is based on two main
ideas: a reformulation of the notion of constraint domain and a functorial presentation of our semantics. In particular, the
semantics of a logic program P is defined in terms of three functors: that apply to constraint domains and provide the operational, the least fixpoint and the logical semantics of P, respectively. To be more concrete, the idea is that the application of to a specific constraint solver provides the operational semantics of P that uses this solver; the application of to a specific domain provides the least fixpoint of P over this domain; and, the application of to a theory of constraints provides the logic theory associated to P. In this context, we prove that these three functors are in some sense equivalent.
相似文献
8.
Emanuele Delucchi 《Journal of Algebraic Combinatorics》2007,26(4):477-494
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice
(Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions
which was recently introduced by Hultman (, 2006), together with the complex of G-symmetric phylogenetic trees
. Hultman shows that the complexes
and
are homotopy equivalent and Cohen–Macaulay, and determines the rank of their top homology.
An application of the theory of building sets and nested set complexes by Feichtner and Kozlov (Selecta Math. (N.S.)
10, 37–60, 2004) shows that in fact
is subdivided by the order complex of
. We introduce the complex of Dowling trees
and prove that it is subdivided by the order complex of
. Application of a theorem of Feichtner and Sturmfels (Port. Math. (N.S.)
62, 437–468, 2005) shows that, as a simplicial complex,
is in fact isomorphic to the Bergman complex of the associated Dowling geometry.
Topologically, we prove that
is obtained from
by successive coning over certain subcomplexes. It is well known that
is shellable, and of the same dimension as
. We explicitly and independently calculate how many homology spheres are added in passing from
to
. Comparison with work of Gottlieb and Wachs (Adv. Appl. Math.
24(4), 301–336, 2000) shows that
is intimely related to the representation theory of the top homology of
.
Research partially supported by the Swiss National Science Foundation, project PP002-106403/1. 相似文献
9.
In [2] the subconstruct of sober approach spaces was introduced and it was shown to be a reflective subconstruct of the category of approach spaces. The main result of this paper states that moreover is firmly -reflective in for the class of epimorphic embeddings. ‘Firm -reflective’ is a notion introduced in [3] by G.C.L. Brümmer and E. Giuli and is inspired by the exemplary behaviour of the usual completion in the category of Hausdorff uniform spaces with uniformly continuous maps. It means that is -reflective in and that the reflector is such that belongs to if and only if is an isomorphism. Firm -reflectiveness implies uniqueness of completion in the sense that whenever is a map with and sober, the associated is an isomorphism. Our result generalizes the fact that in the category the subconstruct of sober topological spaces is firmly reflective for the class of b-dense embeddings in . Also firmness in some other subconstructs of will be easily obtained.A. Gerlo and C. Van Olmen are research assistants at the Fund of Scientific Research Vlaanderen (FWO). E. Vandersmissen is a research assistant supported by the FWO-grant G.0244.05. 相似文献
10.
Libor Barto 《Applied Categorical Structures》2009,17(2):119-152
This paper is a contribution to the theory of functor slices of J. Sichler and V. Trnková. For every ordinal α we introduce a basket , prove that every essentially algebraic category of height α is a slice of , characterize small slices of and give a common generalization of known results about slices of the algebraic basket .
相似文献
11.
G. Zeibig 《Applied Categorical Structures》2006,14(3):215-227
Let and be two monoids (algebras) in a monoidal category . Further let be a distributive law in the sense of [J. Beck, Lect. Notes Math., 80:119–140, 1969]; naturally yields a monoid . Consider a word in the symbols , , and . The first coherence theorem proved in this paper asserts that all morphisms coincide in , provided they arise as composites of morphisms which are -products of ’s ‘canonical’ structure morphisms, and of , , , , , , , and . Assume now that an object is endowed with both an -object structure , and an -object structure . Further assume that these two structures are compatible, in the sense that they naturally yield an -object . Let be a word in , , , and , which contains a single instance of , in the rightmost position. The second coherence theorem states that all morphisms coincide in , provided they arise as composites of morphisms which are -products of ’s ‘canonical’ structure morphisms, and of , , , , , , , , , and . 相似文献
12.
Jean-André Marti 《Acta Appl Math》2009,105(3):267-302
We introduce a general context involving a presheaf
and a subpresheaf ℬ of
. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic
techniques) can be interpretated as the ℬ-local analysis of sections of
.
But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a “frequential
microlocal analysis” and into a “microlocal asymptotic analysis”. The frequential microlocal analysis based on the Fourier
transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in
the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques.
The microlocal asymptotic analysis is a new spectral study of singularities. It can inherit from the algebraic structure of
ℬ some good properties with respect to nonlinear operations.
相似文献
13.
J. Pohjanpelto 《BIT Numerical Mathematics》2008,48(2):337-355
A symmetry-based method for constructing solutions to systems of differential equations founded on the reduction of exterior
differential systems invariant under the action of an infinite dimensional pseudogroup is proposed. One can associate to any
system of differential equations Δ=0 with a symmetry group an exterior differential system invariant under so that solutions of Δ=0 correspond to integral manifolds . The -invariant exterior differential system gives rise to a reduced system specified on a cross section to the pseudogroup orbits, and it is shown that solutions to Δ=0 can be reconstructed from integral
manifolds by solving an equation of generalized Lie type for the jets of pseudogroup transformations. In particular, as opposed to
the classical method of symmetry reduction, every solution to the system of differential equations can, under some mild regularity
assumptions, be constructed by the present algorithm.
AMS subject classification (2000) 58A15, 58A20, 58H05, 58J70 相似文献
14.
We establish an algebra-isomorphism between the complexified Grothendieck ring of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces
of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure
of . As a by-product we obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category
in terms of endomorphisms of the tensor unit of the underlying modular tensor category.
相似文献
15.
Given any R-semimodule M equipped with a semitopology
we construct an N-protosummation
for M. If
satisfies certain properties, then a similar construction leads to an unconditional N-summation
for M, that is an N-summation for M equipped with the trivial prenorm MD over the N-summation (DN,D) for D. Conversely any N-protosummation
on M gives rise to a topology
. If both
and
satisfy a certain separation property, then
and
form a Galois connection.
Dedicated to my friend and collegue Nico Pumplün on the occasion of his 70th birthdayMathematics Subject Classifications (2000) 16Y60, 54A05. 相似文献
16.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2008,151(2):2907-2923
New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists Abelian factors (“rotations”) , and sets of quasi-Jordanian twists . The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra for the composition is a nonminimal parabolic subalgebra in A
n−1 such that . The parabolic twisting elements are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11.
Bibliography: 21 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 187–213. 相似文献
17.
18.
Generalizing the work of Farahat-Higman on symmetric groups, we describe the structures of the even centers
of integral spin symmetric group superalgebras, which lead to universal algebras termed as the spin FH-algebras. A connection
between the odd Jucys-Murphy elements and the Catalan numbers is developed and then used to determine the algebra generators
of the spin FH-algebras and of the even centers
. 相似文献
19.
Béatrice Vedel 《Journal of Fourier Analysis and Applications》2009,15(1):101-123
We propose the construction of wavelet bases with pseudo-polynomials adapted to the homogeneous Sobolev spaces
, s−n/2∈ℕ. They provide a confinement of the infrared divergence by decomposing
as a direct sum X
⊕
Y where X is a “small” space which carries the divergence and Y can be embedded in
. In the case of
we also construct such an orthonormal basis, which provides a confinement of the Mumford process. 相似文献
20.
Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its
nilpotent commutator is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with is dense in . We prove that map given by is an idempotent map. This answers a question of Basili and Iarrobino [9] and gives a partial answer to a question of Panyushev [18]. In the proof, we use the fact that for a generic matrix the algebra generated by A and B is a Gorenstein algebra. Thus, a generic pair of commuting nilpotent matrices generates a Gorenstein algebra. We also describe
in terms of λ if has at most two parts. 相似文献