On the abstract wrapped Floer setups

Abstract

The wrapped Fukaya category of a Liouville sector is defined via an axiomatic construction from the associated abstract wrapped Floer setup. In this paper, we propose a modified axiomatic construction, removing the irrelevant choices and the factorization axiom from the abstract wrapped Floer setup. Based on our modification, we reformulate and then prove a conjecture which essentially claims that the wrapped Fukaya category is obtained as the infinity categorical localization along continuation maps. This amounts to compare the two axiomatic constructions.