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2008 | 6 | 1 | 25-42
Tytuł artykułu

Compact corigid objects in triangulated categories and co-t-structures

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Języki publikacji
EN
Abstrakty
EN
In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, $$ C $$, of a triangulated category, $$ \mathcal{T} $$, which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on $$ \mathcal{T} $$ whose heart is equivalent to Mod(End($$ C $$)op). Rigid objects in a triangulated category can the thought of as behaving like chain differential graded algebras (DGAs). Analogously, looking at objects which behave like cochain DGAs naturally gives the dual notion of a corigid object. Here, we see that a compact corigid object, $$ \mathcal{S} $$, of a triangulated category, $$ \mathcal{T} $$, induces a structure similar to a t-structure which we shall call a co-t-structure. We also show that the coheart of this non-degenerate co-t-structure is equivalent to Mod(End($$ \mathcal{S} $$)op), and hence an abelian subcategory of $$ \mathcal{T} $$.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
1
Strony
25-42
Opis fizyczny
Daty
wydano
2008-03-01
online
2008-02-26
Twórcy
Bibliografia
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  • [11] Hoshino M., Kato Y., Miyachi J., On t-structures and torsion theories induced by compact objects, J. Pure Appl. Algebra, 2002, 167, 15–35 http://dx.doi.org/10.1016/S0022-4049(01)00012-3
  • [12] Iyama O., Yoshino Y., Mutations in triangulated categories and rigid Cohen-Macaulay modules, preprint available at http://arxiv.org/abs/math/0607736
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  • [17] Rotman J.J., An introduction to algebraic topology, Graduate Texts in Mathematics 119, Springer-Verlag, New York, 1988
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0003-2
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