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31.
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
32.
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
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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
35.
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
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38.
Methods of internal-category theory are applied to show that the split epimorphisms in a category C are exactly the morphisms which are effective for descent with respect to any fibration over C (or to any C-indexed category). In the same context, composition-cancellation rules for effective descent morphisms are established and being applied to (suitably defined) locally-split epimorphisms. 相似文献
39.
In this article we carry on the study of the fundamental category (Goubault and Raussen, Dihomotopy as a tool in state space
analysis. In: Rajsbaum, S. (ed.) LATIN 2002: Theoretical Informatics. Lecture Notes in Computer Science, vol. 2286, Cancun,
Mexico, pp. 16–37, Springer, Berlin Heidelberg New York, 2002; Goubault, Homology, Homotopy Appl., 5(2): 95–136, 2003) of a partially ordered topological space (Nachbin, Topology and Order, Van Nostrand, Princeton, 1965; Johnstone, Stone Spaces, Cambridge University Press, Cambridge, MA, 1982), as arising in e.g. concurrency theory (Fajstrup et al., Theor. Comp. Sci. 357: 241–278, 2006), initiated in (Fajstrup et al., APCS, 12(1): 81–108, 2004). The “algebra” of dipaths modulo dihomotopy (the fundamental category) of such a po-space is essentially finite in a number
of situations. We give new definitions of the component category that are more tractable than the one of Fajstrup et al. (APCS,
12(1): 81–108, 2004), as well as give definitions of future and past component categories, related to the past and future models of Grandis (Theory
Appl. Categ., 15(4): 95–146, 2005). The component category is defined as a category of fractions, but it can be shown to be equivalent to a quotient category,
much easier to portray. A van Kampen theorem is known to be available on fundamental categories (Grandis, Cahiers Topologie
Géom. Différentielle Catég., 44: 281–316, 2003; Goubault, Homology, Homotopy Appl., 5(2): 95–136, 2003), we show in this paper a similar theorem for component categories (conjectured in Fajstrup et al. (APCS, 12(1): 81–108,
2004). This proves useful for inductively computing the component category in some circumstances, for instance, in the case of
simple PV mutual exclusion models (Goubault and Haucourt, A practical application of geometric semantics to static analysis
of concurrent programs. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005 – Concurrency Theory: 16th International Conference,
San Francisco, USA, August 23–26. Lecture Notes in Computer Science, vol. 3653, pp. 503–517, Springer, Berlin Heidelberg New
York, 2005), corresponding to partially ordered subspaces of R
n
minus isothetic hyperrectangles. In this last case again, we conjecture (and give some hints) that component categories enjoy
some nice adjunction relations directly with the fundamental category.
相似文献
40.