I will discuss the equivalence of two proposals for constructing an emergent de Sitter space on a 2D CFT, referred to as 'kinematic space'. Special attention is given to the case of a thermal CFT with a BTZ dual. This is based on 1604.02687. The key observation behind the equivalence is the fact that the entanglement entropy behaves as a Liouville field. I will point out how the two proposals have recently converged (in 1604.03110 and 1606.03307) into a generalized notion of kinematic space as the space of pairs of CFT points.