  We present key initial results in the study of global timelike curvature
bounds within the Lorentzian pre-length space framework. Most notably, we
construct a Lorentzian analogue to Alexandrov's Patchwork, thus proving that
suitably nice Lorentzian pre-length spaces with local upper timelike curvature
bound also satisfy a corresponding global upper bound. Additionally, for spaces
with global lower bound on their timelike curvature, we provide a Bonnet-Myers
style result, constraining their finite diameter. Throughout, we make the
natural comparisons to the metric case, concluding with a discussion of
potential applications and ongoing work.
