Uniqueness of Exact Borel Subalgebras and Bocses

Julian Kulshammer, Uppsala University, Sweden. Vanessa Miemietz, University of East Anglia, Norwich, United Kingdom

1. Introduction 2. $A_\infty $-algebras, Kadeishvili's theorem and Merkulov's construction 3. Quasi-hereditary algebras and bocses 4. $A_\infty $-structures on Ext-algebras and uniqueness of bocses A. The lift of the comultiplication $\mu _2$ on $\mathcal {P}$ B. The homotopy $\mu _3$ on $\mathcal {P}$ up to which $\mu _2$ is coassociative C. The maps $\mu _4^0, \mu _4^1, \mu _4^2$ on $\mathcal {P}$ D. The maps $\mu _5^0$ and $\mu _5^1$ on $\mathcal {P}$ E. The map $\mu _6^0$ on $\mathcal {P}$