The lower central series spectral sequence is a particular form of unstable Adams spectral sequence defined by Curtis in 1963. I will describe a categorification of this spectral sequence, which gives a category of 'synthetic spaces' interpolating between pointed connected spaces and restricted Lie algebras. An appealing feature is the existence of an EHP sequence in this setting; this can be used to study the classical EHP spectral sequence using Curtis' (far more computable) algebraic EHP spectral sequence.