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

• Autorzy: David Pauksztello
• 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 $$ \mathcal{T} $$.

Słowa kluczowe

EN

Triangulated category; rigid and corigid object; t-structure; co-t-structure; cochain DGA

Kategorie tematyczne

• 18E40: Torsion theories, radicals
• 18E30: Derived categories, triangulated categories
• 16E45: Differential graded algebras and applications

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 1
• Strony: 25-42

Daty

wydano

2008-03-01

online

2008-02-26

Twórcy

autor

David Pauksztello

• University of Leeds

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-008-0003-2