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math.CT2025
How to invert well-pointed endofunctors
Matt Booth
In this short note we observe that Kelly's transfinite construction of free algebras yields a way to invert well-pointed endofunctors. In enriched settings, this recovers construct…
math.RT2025
Reflexive dg categories in algebra and topology
Matt Booth, Isambard Goodbody, Sebastian Opper
Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Ho…
math.RA2025
Nonsmooth Calabi-Yau structures for algebras and coalgebras
Matt Booth, Joseph Chuang, Andrey Lazarev
We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Sim…