On the abstract wrapped Floer setups

TL;DR

This paper refines the axiomatic construction of the wrapped Fukaya category for Liouville sectors, proving it can be obtained via localization along continuation maps, thus clarifying its foundational structure.

Contribution

It introduces a modified axiomatic framework that removes unnecessary choices and proves the wrapped Fukaya category arises as an infinity categorical localization.

Findings

The modified axiomatic construction simplifies the original framework.

The wrapped Fukaya category is shown to be an infinity categorical localization.

Comparison between two axiomatic constructions is established.

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.