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

Open Mathematics (2008)

- Volume: 6, Issue: 1, page 25-42
- ISSN: 2391-5455

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topDavid Pauksztello. "Compact corigid objects in triangulated categories and co-t-structures." Open Mathematics 6.1 (2008): 25-42. <http://eudml.org/doc/269400>.

@article{DavidPauksztello2008,

abstract = {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 \[ \mathcal \{T\} \]
.},

author = {David Pauksztello},

journal = {Open Mathematics},

keywords = {Triangulated category; rigid and corigid object; t-structure; co-t-structure; cochain DGA; triangulated category; rigid object; corigid object},

language = {eng},

number = {1},

pages = {25-42},

title = {Compact corigid objects in triangulated categories and co-t-structures},

url = {http://eudml.org/doc/269400},

volume = {6},

year = {2008},

}

TY - JOUR

AU - David Pauksztello

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

JO - Open Mathematics

PY - 2008

VL - 6

IS - 1

SP - 25

EP - 42

AB - 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 \[ \mathcal {T} \]
.

LA - eng

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

UR - http://eudml.org/doc/269400

ER -

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