What question did this study set out to answer?

This study aims to establish a condition that determines when a proper DG-category is reflexive according to Kuznetsov and Shinder's framework.

March 24, 2026Open Access

Approximable Triangulated Categories and Reflexive DG-categories

Key Points

This study aims to establish a condition that determines when a proper DG-category is reflexive according to Kuznetsov and Shinder's framework.
Utilized the theory of approximable triangulated categories
Provided a description of the completion of approximable triangulated categories under properness assumptions
Applied findings to various structures including proper schemes and DG-algebras
Clarified conditions for reflexivity in proper DG-categories
Presented applications in the context of proper schemes and Azumaya algebras
Included an appendix showing that certain DG-algebras have finite dimensional models over fields

Abstract

Abstract We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable triangulated category under a properness assumption. We apply our results to proper schemes, proper connective DG-algebras and Azumaya algebras over proper schemes. We include an appendix by Raedschelders and Stevenson showing that proper connective DG-algebras admit finite dimensional models over any field.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Cite this study

Isambard Goodbody (Sun,) studied this question.

synapsesocial.com/papers/69c22975aeb5a845df0d3dfd — DOI: https://doi.org/10.1007/s10485-026-09856-0

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

The homotopy theory of dg-categories and derived Morita theory· 2006 · 467 citations
Construction of 𝑡-structures and equivalences of derived categories· 2003 · 76 citations
Deformation theory of objects in homotopy and derived categories II: Pro-representability of the deformation functor· 2009 · 25 citations
Proper connective differential graded algebras and their geometric realizations· 2022 · 7 citations
Finite-dimensional differential graded algebras and their geometric realizations· 2020 · 19 citations

Authors

Isambard Goodbody

University of Glasgow

Journals

Applied Categorical Structures

Actions

Institutions

University of Glasgow

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Approximable Triangulated Categories and Reflexive DG-categories

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Also consider

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Also consider