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Cluster characters for 2-Calabi–Yau triangulated categories

Yann Palu (2008)

Annales de l’institut Fourier

Starting from an arbitrary cluster-tilting object $T$ in a 2-Calabi–Yau triangulated category over an algebraically closed field, as in the setting of Keller and Reiten, we define, for each object $L$ , a fraction $X (T, L)$ using a formula proposed by Caldero and Keller. We show that the map taking $L$ to $X (T, L)$ is a cluster character, i.e. that it satisfies a certain multiplication formula. We deduce that it induces a bijection, in the finite and the acyclic case, between the indecomposable rigid objects of the cluster...

Coherent functors in stable homotopy theory

Henning Krause (2002)

Fundamenta Mathematicae

Coherent functors 𝓢 → Ab from a compactly generated triangulated category into the category of abelian groups are studied. This is inspired by Auslander's classical analysis of coherent functors from a fixed abelian category into abelian groups. We characterize coherent functors and their filtered colimits in various ways. In addition, we investigate certain subcategories of 𝓢 which arise from families of coherent functors.

Coherent prohomotopical algebra

Timothy Porter (1977)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Cohomology without projectives

Dominique Bourn, Diana Rodelo (2007)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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

David Pauksztello (2008)

Open Mathematics

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, $𝒯$ , 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 $𝒯$ 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...