  In his proof of the K(pi,1) conjecture for complex reflection arrangements,
Bessis defined Garside categories suitable for studying braid groups of
centralizers of Springer regular elements in well-generated complex reflection
groups. We provide a detailed study of these categories, which we call Springer
categories.
  We describe in particular the conjugacy of braided reflections of regular
centralizer in terms of the Garside structure of the associated Springer
category. In so doing we obtain a pure Garside theoretic proof of a theorem of
Digne, Marin and Michel on the center of finite index subgroups in complex
braid groups in the case of a regular centralizer in a well-generated group. We
also provide a "Hurwitz-like" presentation of Springer categories. To this aim
we provide additional insights on noncrossing partitions in the infinite
series. Lastly, we use this "Hurwitz-like" presentation, along with a
generalized Reidemeister-Schreier method we introduce for groupoids, to deduce
nice presentations of the complex braid group B(G31).
