Wrapped A-Infinity Categories Of Legendrians

I will explain an in-preparation project defining a unital A-infinity category of Legendrians associated to any contact manifold admitting an augmentation, via SFT-type holomorphic curves. The objects are, morally, pairs of a Legendrian and an augmentation of their Chekanov-Eliashberg dga. The category is similar to the wrapped Fukaya category of a Liouville manifold: features such as covariant functoriality, stops and stop removal all have analogues. Some enumerative conjectures about the existence of Reeb chords can be rephrased in categorical, and the hope is that locality/descent properties will be useful for acquiring new topological and dynamical results.