  We investigate the problem of finding a pure spin-connection formulation of
General Relativity with non-vanishing cosmological constant. We first revisit
the problem at the linearised level and find that the pure spin-connection,
quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the
square of a Weyl-like tensor. Upon Hodge dualisation, we show that the dual
gauge field in (A)dS$_D$ transforms under $GL(D)$ in the same representation as
a massive graviton in the flat spacetime of the same dimension. We give a
detailed proof that the physical degrees of freedom indeed correspond to a
massless graviton propagating around the (anti-) de Sitter background and
finally speculate about a possible nonlinear pure-connection theory dual to
General Relativity with cosmological constant.
