scholarly journals Relative rigid objects in triangulated categories

2019 ◽  
Vol 520 ◽  
pp. 171-185 ◽  
Author(s):  
Changjian Fu ◽  
Shengfei Geng ◽  
Pin Liu
Keyword(s):  
Triangulated Categories ◽  
Rigid Objects

scholarly journals NEARLY MORITA EQUIVALENCES AND RIGID OBJECTS

2016 ◽  
Vol 225 ◽  
pp. 64-99 ◽  
Author(s):  
ROBERT J. MARSH ◽  
YANN PALU
Keyword(s):  
Simple Module ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Morita Equivalent ◽  
Rigid Objects ◽  
Endomorphism Algebras ◽  
Tilted Algebras ◽  
Calculus Of Fractions ◽  
Cluster Tilting ◽  
Maximal Rigid Object

If $T$ and $T^{\prime }$ are two cluster-tilting objects of an acyclic cluster category related by a mutation, their endomorphism algebras are nearly Morita equivalent (Buan et al., Cluster-tilted algebras, Trans. Amer. Math. Soc. 359(1) (2007), 323–332 (electronic)); that is, their module categories are equivalent “up to a simple module”. This result has been generalized by Yang, using a result of Plamondon, to any simple mutation of maximal rigid objects in a 2-Calabi–Yau triangulated category. In this paper, we investigate the more general case of any mutation of a (non-necessarily maximal) rigid object in a triangulated category with a Serre functor. In that setup, the endomorphism algebras might not be nearly Morita equivalent, and we obtain a weaker property that we call pseudo-Morita equivalence. Inspired by Buan and Marsh (From triangulated categories to module categories via localization II: calculus of fractions, J. Lond. Math. Soc. (2) 86(1) (2012), 152–170; From triangulated categories to module categories via localisation, Trans. Amer. Math. Soc. 365(6) (2013), 2845–2861), we also describe our result in terms of localizations.

scholarly journals RigidFusion: Robot Localisation and Mapping in Environments with Large Dynamic Rigid Objects

2021 ◽  
pp. 1-1
Author(s):  
Ran Long ◽  
Christian Rauch ◽  
Tianwei Zhang ◽  
Vladimir Ivan ◽  
Sethu Vijayakumar
Keyword(s):  
Rigid Objects

scholarly journals Recollements, comma categories and morphic enhancements

2021 ◽  
pp. 1-25
Author(s):  
Xiao-Wu Chen ◽  
Jue Le
Keyword(s):  
Module Category ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Comma Category ◽  
The Right ◽  
Projective Lines ◽  
Triangle Functor

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the category on the left. For a morphic enhancement of a triangulated category $\mathcal {T}$ , there are three explicit ideals of the enhancing category, whose corresponding factor categories are all equivalent to the module category over $\mathcal {T}$ . Examples related to inflation categories and weighted projective lines are discussed.

Learning to predict how rigid objects behave under simple manipulation

2011 ◽  
Author(s):  
Marek Kopicki ◽  
Sebastian Zurek ◽  
Rustam Stolkin ◽  
Thomas Morwald ◽  
Jeremy Wyatt
Keyword(s):  
Rigid Objects ◽  
Simple Manipulation

scholarly journals Comparing Optical Flow Algorithms Using 6-DOF Motion of Real-World Rigid Objects

2012 ◽  
Vol 42 (6) ◽  
pp. 1752-1762 ◽  
Author(s):  
Marco Mammarella ◽  
Giampiero Campa ◽  
Mario L. Fravolini ◽  
Marcello R. Napolitano
Keyword(s):  
Optical Flow ◽  
Real World ◽  
Rigid Objects
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