共查询到20条相似文献,搜索用时 31 毫秒
1.
Harvey Wolff 《manuscripta mathematica》1975,16(3):203-228
We prove a pushout theorem for localizations and Kleisli categories over a symmetric monoidal closed categoryV. That is, suppose is aV-localizable subcategory of aV-categoryA and thatT=(T,,) is aV-monad onA. Then under suitable relations betweenT and we show that there is aV-monadT induced onA[-1] such that the Kleisli category ofT is the pushout of the localization functor :AA[-1] and the free functor F:AK(T). Consequently,K(T)K(T) [S-1] for some S K(T). We give several examples of this situation. 相似文献
2.
Shiqi Song 《Potential Analysis》1994,3(4):391-422
LetE be a rigid separable Banach space andm a bounded Borel measure onE. Let Ext denote the family of all gradient type Dirichlet forms onL
2(E, m) such that the domain of their extended generators (cf. Definition 1.1) contain the smooth functions. We prove three results. First, we prove the existence of the maximum element in Ext whenever Ext is not empty. Secondly, let be the maximum element in Ext (when Ext Ø) and let be a positive function in D(). We define a new measure =2·m and we consider the family Ext associated with the measure . We prove that if is associated with a diffusion process, Ext is not empty and its maximum element is also associated with a diffusion process. Finally, whenm is a centered Gaussian measure onE, we can prove that Ext contains exactly one element. 相似文献
3.
Generalizations of right adjointness (i.e. having a left adjoint) of a functor G:AX are studied. G is called weakly right adjoint, if for any X ObX there exists an AX ObA and an arrow eX:X GAX, such that for any f:XGB there is a (not necessarily unique) morphism f:AXB inA with (Gf)ex=f. As weakly right adjoint functors do not have so many interesting properties, it is useful to consider weakly right adjoint functors with a certain uniqueness condition. There are three ways for doing this, first by assuming uniqueness only for special f' s, second by assuming uniquness only up to automorphisms, and third by assuming a canonical choice of f. A different way of generalizing right adjointness are the locally adjunctable functors of Kaput [5]. These weaker notions of adjointness are compared, their continuity properties are studied and the problem, when they imply right adjointness is discussed. 相似文献
4.
Fangjun H. Arroyo 《Applied Categorical Structures》1997,5(4):339-362
We introduce a theory of coherence for symmetric monoidal categories inthe spirit of Segal and show that it is equivalent, in an appropriate sense,to MacLanes original notion. More precisely, we prove thatspecial categories, the analogue ofspecial spaces, and coherently symmetric monoidalcategories are one and the same. This is analogous to the situation intopology where special spaces are precisely homotopicalcommutative monoids. In light of the obervation that the category of smallcategories Cat bears a functorial Quillen model structure with respect tothe class of categorical equivalences: in fact, is a homotopy theory in thesense of Heller, we may reinterpret the theorem as stating that coherentlysymmetric monoidal categories are precisely the homotopical commutativemonoids within this new homotopy theory. 相似文献
5.
Rudolf Netzsch 《manuscripta mathematica》1971,4(4):305-317
Let K be a field and let Kn denote an n-dimensional affine space over K, where n is a natural number. LetG(K) be the category with the objects Kn (for all n) and the morphisms the affine maps. We callG(K) the affine geometry over K. We give a system of axioms all formulated only with categorical notions like direct product, direct sum, generator etc. We shall prove, that for each categoryC satisfying these axioms there is exactly one field K(C) (up to an isomorphism) such that there is an isomorphism of categoriesG(K(C))C. 相似文献
6.
Peter Schauenburg 《Applied Categorical Structures》1998,6(2):193-222
It is a key property of bialgebras that their modules have a natural tensor product. More precisely, a bialgebra over k can be characterized as an algebra H whose category of modules is a monoidal category in such a way that the underlying functor to the category of k-vector spaces is monoidal (i.e. preserves tensor products in a coherent way). In the present paper we study a class of algebras whose module categories are also monoidal categories; however, the underlying functor to the category of k-vector spaces fails to be monoidal. Instead, there is a suitable underlying functor to the category of B-bimodules over a k-algebra B which is monoidal with respect to the tensor product over B. In other words, we study algebras L such that for two L-modules V and W there is a natural tensor product, which is the tensor product VBW over another k-algebra B, equipped with an L-module structure defined via some kind of comultiplication of L. We show that this property is characteristic for ×B-bialgebras as studied by Sweedler (for commutative B) and Takeuchi. Our motivating example arises when H is a Hopf algebra and A an H-Galois extension of B. In this situation, one can construct an algebra L:=L(A,H), which was previously shown to be a Hopf algebra if B=k. We show that there is a structure theorem for relative Hopf bimodules in the form of a category equivalence
. The category on the left hand side has a natural structure of monoidal category (with the tensor product over A) which induces the structure of a monoidal category on the right hand side. The ×B-bialgebra structure of L that corresponds to this monoidal structure generalizes the Hopf algebra structure on L(A,H) known for B=k. We prove several other structure theorems involving L=L(A,H) in the form of category equivalences
. 相似文献
7.
Shiqi Song 《应用数学学报(英文版)》1993,9(2):115-124
LetX be the solution of the SDE:dX
t = (X
t)dB
t +b(X
t)dt, with andb C
b
(R) such that >0 for some constant , andB a real Brownian motion. Let be the law ofX onE=C([0, 1],R) andk E* – {0}, whereE* is the topological dual space ofE. Consider the classical form:
k
(u, v)=u / kv / kd, whereu andv are smooth functions onE. We prove that, if
k
is closable for anyk in a dense subset ofE* and if the smooth functions are contained in the domain of the generator of the closure of
k
, must be a constant function. 相似文献
8.
Rodney Nillsen 《Monatshefte für Mathematik》1992,114(1):77-82
A special case of the main result proved in this paper is the following. IfG is a locally compact, -compact, non-compact connected abelian group, thenL
2
(G)={f–*f:fL
2
(G), L
1
(G), 0 and
G
=1}. In this case, any topologically invariant linear form onL
2
(G) is 0. 相似文献
9.
Geoffery M.L. Powell 《K-Theory》1998,13(3):279-304
This paper defines and studies the polynomial filtration [pk
] of the shift functor
: F , where F is the category of functors between F-vector spaces over a finite field F. The functors [pk
] correspond to a system of functors (pk T):U U, related to Lannes'T-functor on the category U of unstable modules over the Steenrod algebra. The main results concern the behaviour of the quotients ~ s:=~/[ps-1~ filtrations by ~s-nilpotent functors are introduced and it is shown that the full subcategory of
s-nilpotent functors is thick. 相似文献
10.
S. V. Solov'ev 《Journal of Mathematical Sciences》1982,20(4):2367-2369
We consider the (&, )-fragment of the intuitionistic propositional calculus. It is proved that under the standard transformation of a Gentzen derivation into a natural derivation(), the length of (())22·length(
). There is constructed a sequence of Gentzen derivations of length i, for which the length of ((
i))21/3·length(i), which shows that the upper bound obtained is not too weak.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 192–196, 1979. 相似文献
11.
H. Scheerer 《manuscripta mathematica》1985,51(1-3):63-87
Let R be a subring of the rationals with 1/2, 1/3R; let S
R
n
denote the R-local n-sphere and define
R
n
:=S
R
n
for n odd,
R
n
:=S
R
n
for n>0 even. An H-space (resp. a 1-conn. co-H-space) is decomposable over R, if it is homotopy equivalent to a weak product of spaces
R
n
(resp. to a wedge of R-local spheres). We prove that, if E is grouplike decomposable of finite type over R, the functor [-,E] is determined on finite dim. complexes by the Hopf algebra M*(E;R); here M* denotes the unstable cohomotopy functor of H.J. Baues. If C is cogrouplike decomposable over R, the functor [C,-] is determined on 1-conn. R-local spaces by *(C) as a cogroup in the category of M-Lie algebras. For R = the functor [-,E] is also determined by the Lie algebra *(E) and [C,-] by the Berstein coalgebra associated to the comultiplication of C. 相似文献
12.
LetV be a finite dimensional complex linear space and letG be a compact subgroup of GL(V). We prove that an orbitG, V, is polynomially convex if and only ifG
is closed andG is the real form ofG
. For every orbitG which is not polynomially convex we construct an analytic annulus or strip inG
with the boundary inG. It is also proved that the group of holomorphic automorphisms ofG
which commute withG
acts transitively on the set of polynomially convexG-orbits. Further, an analog of the Kempf-Ness criterion is obtained and homogeneous spaces of compact Lie groups which admit only polynomially convex equivariant embeddings are characterized.Supported by Federal program Integratsiya, no. 586.Supported by INTAS grant 97/10170. 相似文献
13.
《Quaestiones Mathematicae》2013,36(4):391-411
Abstract Given a monoidal category B and a category S of monoids in B we study the category MODS of all actions of monoids from S on B-objects. This is mainly done by investigation of the underlying functor V: MODS → SxB. In particular V creates limits; filtered colimits and arbitrary colimits are detected, provided the monoidal structure behaves nicely with respect to these constructions. Moreover MODS contains B as a full coreflective subcategory; S is contained as a full reflective (and coreflective) one provided B has a terminal (zero) object. Monadicity of MODS over B is discussed as well. 相似文献
14.
Wolfgang Hein 《manuscripta mathematica》1985,52(1-3):97-130
Pair algebras which have a non degenerate (left- and right-) invariant bilinear form and for which the inner derivation algebra is completely reducible are characterised by pairs (C,), where C is a n×n matrix satisfying certain conditions and is a sequence of n integers equal to 0 or 1. They occur as pair algebras of type (S(C,)–1,S(C,)1), xuy=[[x,u],y], where (S(C,)r)r is the gradation induced by . in the Kac-Moody algebraS(C). If C is an affin Cartan matrix (as in the case of Lie triple systems), there exists a finite dimensional simple Lie algebrag and a Aut (g), ord =m< such that the pair algebra is isomorphic to the pair algebra (g
–1,g
1), xuy=[[x,u],y] (product ing), whereg
i. is the eigenspace of of eigenvalue i, a primitive m-th root of unity. 相似文献
15.
Eli Katz 《Annali di Matematica Pura ed Applicata》1989,154(1):1-11
Summary We would like to monitor the homotopy type of the loop space of mapping cones (Y tf CX) for X and Y fixed and varying f. The effect of f on the homotopy type is reflected by the cooperation of the loop space of the mapping cone induced by the usual cooperation of the mapping cone Y tfCX Y tfCXX. Using the singular complex functor we move to the category of differential graded algebras. Motivated by the cooperation of the loop space of the mapping cone we define a free co-module. We find universal objects in this category and two classification theorems. 相似文献
16.
We obtain the analytic expression for the total cross section of the reaction e
–
e
+l
–
l
+ (l=,) taking possible quasianapole interaction effects into account. We find numerical restrictions on the interaction parameter value from data for the reaction e
–
e
+–+ in the energy domain below the Z
0 peak. 相似文献
17.
Ju¨rg Hu¨sler 《Extremes》1999,2(1):59-70
Consider a triangular array of standard Gaussian random variables {n,i, i 0, n 1} such that {n,i, i 0} is a stationary normal sequence for each n 1. Let n,k = corr(n,i,n,i+k). If (1-n,k)log n k (0,) as n for some k, then the locations where the extreme values occur cluster and the limiting distribution of the maxima is still the Gumbel distribution as in the stationary or i.i.d. case, but shifted by a parameter measuring the clustering. Triangular arrays of Gaussian sequences are used to approximate a continuous Gaussian process X(t), t 0. The cluster behavior of the random sequence refers to the behavior of the extremes values of the continuous process. The relation is analyzed. It reveals a new definition of the constants H
used for the limiting distribution of maxima of continuous Gaussian processes and provides further understanding of the limit result for these extremes. 相似文献
18.
Jens-Uwe Mertens 《manuscripta mathematica》1973,9(4):357-374
It is shown that the category of chain-complexes (of abelian groups) can be embedded as a full reflexive subcategory in the categoryEC of semi-regular exact couples. This situation gives rise to a monad on the categoryEC which has similar properties as the infinite symmetric product [4]. We use this monad and the process of Kan-extensions to study connections between the homology- and homotopyfunctors defined onEC. Furthermore we investigate homotopy-notions inEC and demonstrate that those constructed by W.S. Massey [9] and D.W. Kahn [6] are equivalent. 相似文献
19.
Tin-Yau Tam 《Monatshefte für Mathematik》1986,101(3):245-252
LetV be ann-dimensional inner product space,T
i
,i=1,...,k, k linear operators onV, H a subgroup ofS
m
(the symmetric group of degreem), a character of degree 1 andT a linear operator onV. Denote byK(T) the induced operator ofT onV
(H), the symmetry class of tensors associated withH and . This note is concerned with the structure of the setK
, m
H
(T1,...,Tk) consisting of all numbers of the form traceK(T
1
U
1...T
k
U
k
) whereU
i
,i=1,...k vary over the group of all unitary operators onV. For V=n or n, it turns out thatK
, m
H
(T1,...,Tk) is convex whenm is not a multiple ofn. Form=n, there are examples which show that the convexity of
, m
H
(T1,...,Tk) depends onH and .The author wishes to express his thanks to Dr. Yik-Hoi Au-Yeung for his valuable advice and encouragement. 相似文献
20.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献