Cyclic posets and triangulation clusters
Kiyoshi Igusa,Gordana Todorov +1 more
TLDR
In this paper, a generalization of the constructions of various triangulated categories with cluster structures is presented, called triangulation clusters, which are those corresponding to topological triangulations of the 2-disk.Abstract:
Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures. We give an overview, and then analyze “triangulation clusters” which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the “cactus space” associated to the “cactus cyclic poset”.read more
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Feynman categories and Representation Theory
TL;DR: Feynman categories as discussed by the authors are a special type of monoidal categories and their representations are monoidal functors, which can be viewed as a far reaching generalization of groups, algebras and modules.
References
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Journal ArticleDOI
Cluster structures for 2-Calabi-Yau categories and unipotent groups
TL;DR: In this paper, the authors investigated cluster-tilting objects in triangulated 2-Calabi-Yau and related categories, including pre-projective algebras of non-Dynkin quivers.
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Cluster structures for 2-Calabi-Yau categories and unipotent groups
TL;DR: In this paper, the authors investigated cluster tilting objects in triangulated 2-Calabi-Yau categories and related categories, such as pre-projective algebras of non-Dynkin quivers associated with elements in the Coxeter group.
Journal ArticleDOI
Mutation of cluster-tilting objects and potentials
TL;DR: In this article, it was shown that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials.
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Mutation of cluster-tilting objects and potentials
TL;DR: In this article, it was shown that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials.
Journal ArticleDOI
On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon
Thorsten Holm,Peter Jørgensen +1 more
TL;DR: In this paper, it was shown that there is a bijection between the cluster tilting subcategories of a k-linear algebraic triangulated category and certain triangulations of the ∞-gon.