Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Compact corigid objects in triangulated categories and co-t-structures
AU - Pauksztello, David
PY - 2008/3
Y1 - 2008/3
N2 - In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, CC , of a triangulated category, TT , 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 TT whose heart is equivalent to Mod(End( CC )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, SS , of a triangulated category, TT , 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( SS )op), and hence an abelian subcategory of TT .
AB - In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, CC , of a triangulated category, TT , 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 TT whose heart is equivalent to Mod(End( CC )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, SS , of a triangulated category, TT , 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( SS )op), and hence an abelian subcategory of TT .
KW - Triangulated category
KW - rigid and corigid object
KW - t-structure
KW - co-t-structure
KW - cochain DGA
U2 - 10.2478/s11533-008-0003-2
DO - 10.2478/s11533-008-0003-2
M3 - Journal article
VL - 6
SP - 25
EP - 42
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 1
ER -