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1.
We introduce a notion of a subtractive category. It generalizes the notion of a pointed subtractive variety of universal algebras in the sense of A. Ursini. Subtractive categories are closely related to Mal’tsev and additive categories: (i) a category C with finite limits is a Mal’tsev category if and only if for every object X in C the category Pt(X)=((X,1X)↓(C↓X)) of “points over X” is subtractive; (ii) a pointed category C with finite limits is additive if and only if C is subtractive and half-additive.Mathematics Subject Classifications (2000) 18C99, 18E05, 08B05. 相似文献
2.
Mart Abel 《Rendiconti del Circolo Matematico di Palermo》2008,57(1):83-101
Abstract We define and study the group K(X) of a topological space X as the Grothendieck group of the category of suitable module bundles over X instead of the Grothendieck group of the category of vector bundles over X and prove some of its properties.
Keywords Topological K-Theory, Module bundles, Waelbroeck algebra
Mathematics Subject Classification (2000) 19 Lxx, 19 Axx, (Secondary) 46 Hxx 相似文献
3.
A function J defined on a family C of stationary processes is finitely observable if there is a sequence of functions s
n
such that s
n
(x
1,…, x
n
) → J(X) in probability for every process X=(x
n
) ∈ C. Recently, Ornstein and Weiss proved the striking result that if C is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant defined
on C is entropy [8]. We sharpen this in several ways. Our main result is that if X → Y is a zero-entropy extension of finite entropy ergodic systems and C is the family of processes arising from generating partitions of X and Y, then every finitely observable function on C is constant. This implies Ornstein and Weiss’ result, and extends it to many other families of processes, e.g., it follows
that there are no nontrivial finitely observable isomorphism invariants for processes arising from the class of Kronecker
systems, the class of mild mixing zero entropy systems, or the class of strong mixing zero entropy systems. It also follows
that for the class of processes arising from irrational rotations, every finitely observable isomorphism invariant must be
constant for rotations belonging to a set of full Lebesgue measure.
This research was supported by the Israel Science Foundation (grant No. 1333/04) 相似文献
4.
Let G be a finite group. Given a finite G-set X\cal{X} and a modular tensor category C\cal{C}, we construct a weak G-equivariant fusion category CX\cal{C}^{\cal{X}}, called the permutation equivariant tensor category. The construction is geometric and uses the formalism of modular functors.
As an application, we concretely work out a complete set of structure morphisms for
\mathbbZ/2\mathbb{Z}/2-permutation equivariant categories, finishing thereby a program we initiated in an earlier paper. 相似文献
5.
Yukinobu Toda 《Advances in Mathematics》2008,217(6):2736-2781
For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T. Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D. Joyce's work, we introduce the invariants counting semistable objects in D(X), and show that the invariants are independent of a choice of a stability condition. 相似文献
6.
We show that up to a translation each automorphism of the derived category D b X of coherent sheaves on a weighted projective line X, equiv-alently of the derived category D b A of finite dimensional modules over a derived canonical algebra A, is composed of tubular mutations and automorphisms of X. In the case of genus one this implies that the automorphism group is a semi-direct product of the braid group on three strands by a finite group. Moreover we prove that most automorphisms lift from the Grothendieck group to the derived category. 相似文献
7.
Michał Jerzy Kukieła 《Order》2010,27(1):9-21
We generalise some results of R. E. Stong concerning finite spaces to wider subclasses of Alexandroff spaces. In particular,
we characterize pairs of spaces X,Y such that the compact-open topology on C(X,Y) is Alexandroff, give a homotopy type classification of a class of infinite Alexandroff spaces and prove some results concerning
cores of locally finite spaces. We also discuss a mistake found in an article of F.G. Arenas. Since the category of T
0 Alexandroff spaces is equivalent to the category of posets, our results may lead to a deeper understanding of the notion
of a core of an infinite poset. 相似文献
8.
9.
Manfred Stelzer 《Mathematische Zeitschrift》2007,257(1):81-106
Relations between category and strong category are studied. The notion of a homotopy coalgebra of order r over the Ganea comonad
is introduced. It is shown that cat(X) =Cat(X) holds if a finite 1-connected complex X carries such a structure with r sufficiently large. 相似文献
10.
In this work, lattice isomorphisms of semirings C
+(X) of continuous nonnegative functions over an arbitrary topological space X are characterized. It is proved that any isomorphism of lattices of all subalgebras with a unit of semirings C
+(X) and C
+(Y) is induced by a unique isomorphism of semirings. The same result is also correct for lattices of all subalgebras excepting
the case of two-point Tychonovization of spaces. 相似文献
11.
Y. Chiang 《Journal of Global Optimization》2010,47(1):53-62
Let Z{\mathcal{Z}} be an ordered Hausdorff topological vector space with a preorder defined by a pointed closed convex cone C ì Z{C \subset {\mathcal Z}} with a nonempty interior. In this paper, we introduce exceptional families of elements w.r.t. C for multivalued mappings defined on a closed convex cone of a normed space X with values in the set L(X, Z){L(X, {\mathcal Z})} of all continuous linear mappings from X into Z{\mathcal{Z}} . In Banach spaces, we prove a vectorial analogue of a theorem due to Bianchi, Hadjisavvas and Schaible. As an application,
the C-EFE acceptability of C-pseudomonotone multivalued mappings is investigated. 相似文献
12.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
X ? *\Bbb CX \rightarrow {}{^{\ast}{\Bbb C}}
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
Mw(X)/M0(X){\cal M}_{\omega}(X)/{\cal M}_0(X)
, for certain external subspaces
M0(X), Mw(X){\cal M}_0(X), {\cal M}_{\omega}(X)
of the hyperfinite dimensional Banach space
*\Bbb CX{}{^{\ast}{\Bbb C}}^X
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
Mw(G)/M0(G){\cal M}_{\omega}(G)/{\cal M}_0(G)
are isometrically isomorphic as Banach algebras. 相似文献
13.
Many families of parametrized Thue equations over number fields have been solved recently. In this paper we consider for the
first time a family of Thue equations over a polynomial ring. In particular, we calculate all solutions of
X(X-Y)(X-(T+x)Y)+Y3=1+xT(1-T)X(X-Y)(X-(T+\xi)Y)+Y^3=1+\xi T(1-T)
over
\Bbb C[T]{\Bbb C}[T]
for all
x ? \Bbb C\xi\in{\Bbb C}
. 相似文献
14.
J. Brzdek 《Aequationes Mathematicae》2000,59(3):248-254
Summary. Let \Bbb K {\Bbb K} be either the field of reals or the field of complex numbers, X be an F-space (i.e. a Fréchet space) over \Bbb K {\Bbb K} n be a positive integer, and f : X ? \Bbb K f : X \to {\Bbb K} be a solution of the functional equation¶¶f(x + f(x)n y) = f(x) f(y) f(x + f(x)^n y) = f(x) f(y) .¶We prove that, if there is a real positive a such that the set { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} contains a subset of second category and with the Baire property, then f is continuous or { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} for every x ? X x \in X . As a consequence of this we obtain the following fact: Every Baire measurable solution f : X ? \Bbb K f : X \to {\Bbb K} of the equation is continuous or equal zero almost everywhere (i.e., there is a first category set A ì X A \subset X with f(X \A) = { 0 }) f(X \backslash A) = \{ 0 \}) . 相似文献
15.
Suzanne Larson 《代数通讯》2013,41(8):2611-2627
Let X be a compact topological space and let C(X) denote the f-ring of all continuous real-valued functions defined on X. A point x in X is said to have rank n if, in C(X), there are n minimal prime ?-ideals contained in the maximal ?-ideal M x = {f ? C(X):f(x) = 0}. The space X has finite rank if there is an n ? N such that every point x ? X has rank at most n. We call X an SV space (for survaluation space) if C(X)/P is a valuation domain for each minimal prime ideal P of C(X). Every compact SV space has finite rank. For a bounded continuous function h defined on a cozeroset U of X, we say there is an h-rift at the point z if h cannot be extended continuously to U ∪ {z}. We use sets of points with h-rift to investigate spaces of finite rank and SV spaces. We show that the set of points with h-rift is a subset of the set of points of rank greater than 1 and that whether or not a compact space of finite rank is SV depends on a characteristic of the closure of the set of points with h-rift for each such h. If X has finite rank and the set of points with h-rift is an F-space for each h, then X is an SV space. Moreover, if every x ? X has rank at most 2, then X is an SV space if and only if for each h, the set of points with h-rift is an F-space. 相似文献
16.
It is known that any strict tensor category (C⊗I) determines a braided tensor categoryZ(C), the centre ofC. WhenA is a finite dimension Hopf algebra, Drinfel’d has proved thatZ(A
M) is equivalent to
D(A)
M as a braided tensor category, whereA
M is the left A-module category andD(A) is the Drinfel’d double ofA. For a braided tensor category, the braidC
U,v is a natural isomorphism for any pair of object (U,V) in. If weakening the natural isomorphism of the braidC
U,V to a natural transformation, thenC
U,V is a prebraid and the category with a prebraid is called a prebraided tensor category. Similarly it can be proved that any strict
tensor category determines a prebraided tensor category Z∼ (C), the near centre of. An interesting prebraided tensor structure of the Yetter-Drinfel’d category
C*A
YD
C*A
given, whereC # A is the smash product bialgebra ofC andA. And it is proved that the near centre of Doi-Hopf module
A
M(H)
C
is equivalent to the Yetter-Drinfel’ d
C*A
YD
C*A
as prebraided tensor categories. As corollaries, the prebraided tensor structures of the Yetter-Drinfel’d category
A
YD
A
, the centres of module category and comodule category are given. 相似文献
17.
We will say that a subgroup X of G satisfies property C in G if CG(X?Xg)\leqq X?Xg{\rm C}_{G}(X\cap X^{{g}})\leqq X\cap X^{{g}} for all g ? G{g}\in G. We obtain that if X is a nilpotent subgroup satisfying property C in G, then XF(G) is nilpotent. As consequence it follows that if N\triangleleft GN\triangleleft G is nilpotent and X is a nilpotent subgroup of G then CG(N?X)\leqq XC_G(N\cap X)\leqq X implies that NX is nilpotent.¶We investigate the relationship between the maximal nilpotent subgroups satisfying property C and the nilpotent injectors in a finite group. 相似文献
18.
C. Gasbarri 《Mathematische Annalen》2010,346(1):199-243
We give a generalization of the classical Bombieri–Schneider–Lang criterion in transcendence theory. We give a local notion of LG-germ, which is similar to the notion of E-function and Gevrey condition, and which generalize (and replace) the condition on derivatives in the theorem quoted above. Let ${K \subset \mathbb{C}}We give a generalization of the classical Bombieri–Schneider–Lang criterion in transcendence theory. We give a local notion
of LG-germ, which is similar to the notion of E-function and Gevrey condition, and which generalize (and replace) the condition on derivatives in the theorem quoted above.
Let
K ì \mathbbC{K \subset \mathbb{C}} be a number field and X a quasi-projective variety defined over K. Let γ : M → X be an holomorphic map of finite order from a parabolic Riemann surface to X such that the Zariski closure of the image of it is strictly bigger then one. Suppose that for every p ? X(K)?g(M){p\in X(K)\cap\gamma(M)} the formal germ of M near P is an LG-germ, then we prove that X(K)?g(M){X(K)\cap\gamma(M)} is a finite set. Then we define the notion of conformally parabolic K?hler varieties; this generalize the notion of parabolic
Riemann surface. We show that on these varieties we can define a value distribution theory. The complementary of a divisor
on a compact K?hler manifold is conformally parabolic; in particular every quasi projective variety is. Suppose that A is conformally parabolic variety of dimension m over
\mathbbC{\mathbb{C}} with K?hler form ω and γ : A → X is an holomorphic map of finite order such that the Zariski closure of the image is strictly bigger then m. Suppose that for every p ? X(K)?g(A){p\in X(K)\cap \gamma (A)} , the image of A is an LG-germ. then we prove that there exists a current T on A of bidegree (1, 1) such that òATùwm-1{\int_AT\wedge\omega^{m-1}} explicitly bounded and with Lelong number bigger or equal then one on each point in γ
−1(X(K)). In particular if A is affine γ
−1(X(K)) is not Zariski dense. 相似文献
19.
《代数通讯》2013,41(2):869-875
Abstract Given a contravariant functor F : 𝒞 → 𝒮ets for some category 𝒞, we say that F (𝒞) (or F) is generated by a pair (X, x) where X is an object of 𝒞 and x ∈ F(X) if for any object Y of 𝒞 and any y ∈ F(Y), there is a morphism f : Y → X such that F(f)(x) = y. Furthermore, when Y = X and y = x, any f : X → X such that F(f)(x) = x is an automorphism of X, we say that F is minimally generated by (X, x). This paper shows that if the ring R is left noetherian, then there exists a minimal generator for the functor ?xt (?, M) : ? → 𝒮ets, where M is a left R-module and ? is the class (considered as full subcategory of left R-modules) of injective left R-modules. 相似文献
20.
We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write X ∼ Y if X
p
≅ Y
p
for all prime p, where X
p
denotes the image of Xin the localized category S
p
. We prove that it is equivalent to the stable isomorphism X∨B
0 ≅Y∨B
0, where B
0 is the wedge of all spheres S
n
such that π
n
S
(X) is infinite. We also prove that a stable isomorphism X ∨ X ≅ Y ∨ X implies a stable isomorphism X ≅ Y. 相似文献