  Context. The relationship between outflow launching and formation of
accretion disks around young stellar objects is still not entirely understood,
which is why spectrally and spatially resolved observations are needed.
Recently, the Atacama Large Millimetre/sub-millimetre Array (ALMA) has carried
out long-baseline observations towards a handful of sources, revealing
connections between outflows and the inner regions of disks.
  Aims. Here we aim to determine the small-scale kinematic and morphological
properties of the outflow from the isolated protostar B335 for which no
Keplerian disk has, so far, been observed on scales down to 10 au.
  Methods. We use ALMA in its longest-baseline configuration to observe
emission from CO isotopologs, SiO, SO$_2$ and CH$_3$OH. The proximity of B335
provides a resolution of ~3 au (0.03''). We also combine our long-baseline data
with archival data to produce a high-fidelity image covering scales up to 700
au (7'').
  Results. $^{12}$CO has a X-shaped morphology with arms ~50 au in width that
we associate with the walls of an outflow cavity, similar to what is observed
on larger scales. Long-baseline continuum emission is confined to <7 au of the
protostar, while short-baseline continuum emission follows the $^{12}$CO
outflow and cavity walls. Methanol is detected within ~30 au of the protostar.
SiO is also detected in the vicinity of the protostar, but extended along the
outflow.
  Conclusions. The $^{12}$CO outflow shows no clear signs of rotation at
distances $\gtrsim$30 au from the protostar. SiO traces the protostellar jet on
small scales, but without obvious rotation. CH$_3$OH and SO$_2$ trace a region
<16 au in diameter, centred on the continuum peak, which is clearly rotating.
Using episodic, high-velocity, $^{12}$CO features, we estimate the launching
radius of the outflow to be <0.1 au and dynamical timescales on the order of a
few years.
