منابع مشابه
Naturality of Abel maps
We give a combinatorial characterization of nodal curves admitting a natural (i.e. compatible with and independent of specialization) d-th Abel map for any d ≥ 1. Let X be a smooth projective curve and d a positive integer; the classical d-th Abel map of X , αX : X d −→ PicX , associates to (p1, . . . , pd) ∈ X the class of the line bundle OX(p1 + . . .+ pd) in Pic d X . Such a morphism has goo...
متن کاملNaturality and Definability, I
Eilenberg and Mac Lane [1] explained the notion of a 'natural' embedding by giving a categorical definition. Starting from their examples, we argue that one could equally well explain natural as meaning 'uniformly definable in set theory'. But do the categorically natural embeddings coincide with the uniformly definable ones? This is partly a technical question about whether certain well-known ...
متن کاملLimit Preservation from Naturality
A functor G : C → D is said to preserve limits of a diagram D : I → C if it sends any limiting cone from x to D to a limiting cone from G(x) to G◦D. When G preserves limits of a diagram D this entails directly that there is an isomorphism G(lim ←−ID) ∼= lim ←−I(G ◦D) between objects. In general, such an isomorphism alone is not sufficient to ensure that G preserves limits. This paper shows how,...
متن کاملNaturality and Definability Ii
In two papers [3] and [4] we noted that in common practice many algebraic constructions are defined only ‘up to isomorphism’ rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper provides much fuller answers, though some questions remain open. Our main result, Theorem 4, says that there is a transitive model of Zermelo-Fraen...
متن کاملNaturality and Induced Representations
We show that induction of covariant representations for C∗-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C∗-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green’s Impri...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1996
ISSN: 0022-4049
DOI: 10.1016/0022-4049(95)00136-0