In the setting of Lorentzian pre-length spaces, I will introduce the notion of hyperbolic angles and present the triangle inequality of angles. Furthermore, hyperbolic angles allow us to make an equivalent formulation of timelike curvature bounds, akin to the monotonicity condition in metric spaces. Under timelike curvature bounds, we also proved the continuity of angles. If time permits, I will also mention some results on the space of directions and define the future timelike exponential and logarithmic map.

This is joint work with Clemens Sämann. This work was supported by FWF grant J4305 and P33594.