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31.
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
32.
Jean-Pierre Demailly Jun-Muk Hwang Thomas Peternell 《Journal of Geometric Analysis》2008,18(2):324-340
Let X be a compact complex manifold which is the image of a complex torus by a holomorphic surjective map A→X. We prove that X is Kähler and that up to a finite étale cover, X is a product of projective spaces by a torus. 相似文献
33.
态射的和与积的Moore-Penrose逆 总被引:1,自引:0,他引:1
张京芬 《华中师范大学学报(自然科学版)》1993,32(3):0-0
态射的Moore-Penrose逆是矩阵的Moore-Penrose逆在有对合*的范畴中的推广。本文给出加法范畴及Abel范畴中态射的和与积的Moore-Penrose逆存在的充分条件和一些性质。 相似文献
34.
H.N. Bhattrai 《Geometriae Dedicata》1999,78(2):111-120
Projective geometries studied as Pasch geometries possess morphisms and homomorphisms. A homomorphic image of a projective geometry is shown to be projective. A projective geometry is shown to be Desarguesian iff it is a homomorphic image of a higher dimensional one, which in a sense is dual to the classical imbedding theorem. Semi-linear maps induce morphisms which are homomorphisms iff the associated homomorphisms of skewfields are isomorphisms. Projective geometries form categories with morphisms as well as homomorphisms and Desarguesian ones form a subcategory with Desarguesian homomorphisms. 相似文献
35.
讨论了预加范畴中的态射方程axβ+σyτ=γ,给出了其有解的充要条件和通解公式,并且,对主理想整环上的矩阵方程AXB+CYD=E给出了相应的结论。 相似文献
36.
基于栈操作的用例规模的一个计算公式 总被引:2,自引:0,他引:2
软件测试随着测试用例规模的增加变得十分困难,对测试用例进行研究十分必要.本文首先给出了树同构的概念,然后利用图论就栈操作的用例进行了讨论,并得到一系列有关栈操作用例的重要性质,最后对一个给定任意大小的输入序列,讨论了其各种可能的输出序列,在此基础上得到了各种可能输出序列规模的一个递推计算公式. 相似文献
37.
George Voutsadakis 《Mathematical Logic Quarterly》2009,55(1):51-67
The notion of an ? ‐matrix as a model of a given π ‐institution ? is introduced. The main difference from the approach followed so far in Categorical Abstract Algebraic Logic (CAAL) and the one adopted here is that an ? ‐matrix is considered modulo the entire class of morphisms from the underlying N ‐algebraic system of ? into its own underlying algebraic system, rather than modulo a single fixed (N,N ′)‐logical morphism. The motivation for introducing ? ‐matrices comes from a desire to formulate a correspondence property for N ‐protoalgebraic π ‐institutions closer in spirit to the one for sentential logics than that considered in CAAL before. As a result, in the previously established hierarchy of syntactically protoalgebraic π ‐institutions, i. e., those with an implication system, and of protoalgebraic π ‐institutions, i. e., those with a monotone Leibniz operator, the present paper interjects the class of those π ‐institutions with the correspondence property, as applied to ? ‐matrices. Moreover, this work on ? ‐matrices enables us to prove many results pertaining to the local deduction‐detachment theorems, paralleling classical results in Abstract Algebraic Logic formulated, first, by Czelakowski and Blok and Pigozzi. Those results will appear in a sequel to this paper. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
38.
A classical result of P. Freyd and M. Kelly states that in “good” categories, the Orthogonal Subcategory Problem has a positive
solution for all classes of morphisms whose members are, except possibly for a subset, epimorphisms. We prove that under the same assumptions on the
base category and on , the generalization of the Small Object Argument of D. Quillen holds—that is, every object of the category has a cellular
-injective weak reflection. In locally presentable categories, we prove a sharper result: a class of morphisms is called quasi-presentable
if for some cardinal λ every member of the class is either λ-presentable or an epimorphism. Both the Orthogonal Subcategory Problem and the Small Object Argument are valid for quasi-presentable
classes. Surprisingly, in locally ranked categories (used previously to generalize Quillen’s result), this is no longer true:
we present a class of morphisms, all but one being epimorphisms, such that the orthogonality subcategory is not reflective and the injectivity subcategory Inj is not weakly reflective. We also prove that in locally presentable categories, the injectivity logic and the Orthogonality
Logic are complete for all quasi-presentable classes.
Financial support by Centre for Mathematics of University of Coimbra and by School of Technology of Viseu is acknowledged
by the third author. 相似文献
39.
林喜季 《福州大学学报(自然科学版)》2010,38(3):318-324
考虑AsB的箭图 (Q*, I*) 的自同构由带关系箭图(Q, I)的自同构和带关系箭图 (Q′, I′) 的自同构决定情况, 证明了 AsB的Frobenius态射由 A 的Frobenius态射和 B 的Frobenius态射决定; 代数 AsB 的固定点代数同构于相应的代数 A 的固定点代数与 B 的固定点代数的张量积. 相似文献
40.