  This paper is mainly based on the talk I presented at the meeting "The
Philosophy and Physics of Noether's Theorems" that took place 5-6 October 2018,
but it also contains some original results that were inspired by discussions
with mathematicians, physicists and philosophers about the problem of
understanding the intrinsic meaning of gauge invariance. In this work, I argue
that following the principles of locality, deformation and homology, one
naturally ends up using the Batalin-Vilkovisky (BV) formalism in quantizing
gauge theories.
  I start with the gentle introduction into the BV framework and then I proceed
to some new results and more speculative deliberations. In the classical
theory, I present a new perspective on the classical BV operator, using the
notion of Moller maps. In the quantum theory, I present some loose ideas on the
formulation of anomalous master Ward identity in the framework proposed
recently by Buchholz and Fredenhagen, based on local S-matrices.
