منابع مشابه
Exact Categories Theo Bühler
We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3×3-lemma and the snake lemma. We briefly discuss exact functors, idempotent completion and weak idempotent completeness. We then show that it is possible to construct the derived category of an exact category without any em...
متن کاملExact Categories and Duality
Throughout the book Homological algebra, by H. Cartan and S. Eilenberg, the authors dealt with functors defined on categories of modules over certain rings and whose values again were modules over a ring. It will be shown in this paper that the theory may be generalized to functors defined on abstract categories, and whose values are again in such abstract categories. An abstract treatment such...
متن کاملOn the Cyclic Homology of Exact Categories
The cyclic homology of an exact category was defined by R. McCarthy [17] using the methods of F. Waldhausen [26]. McCarthy’s theory enjoys a number of desirable properties, the most basic being the extension property, i.e. the fact that when applied to the category of finitely generated projective modules over an algebra it specializes to the cyclic homology of the algebra. However, we show tha...
متن کاملExact completion and representations in abelian categories
When the exact completion of a category with weak finite limits is a Mal’cev category, it is possible to combine the universal property of the exact completion and the universal property of the coequalizer completion. We use this fact to explain Freyd’s representation theorems in abelian and Frobenius categories. MSC 2000 : 18A35, 18B15, 18E10, 18G05.
متن کاملExact Sequences and Closed Model Categories
For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences. In this paper, we remove the hypothesis of the existence of zero object and construct (using the category over the initial object or the category under the final object) these sequences for unpointed model categories. We illustrate the power of this result in abstract homotopy t...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2010
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2009.04.004