When brittle hydrogels fail, several mechanisms conspire to alter the state of stress near the tip of a crack, and it is challenging to identify which mechanism is dominant. In the fracture of brittle solids, a sufficient far-field stress results in the complete loss of structural strength as the material 'unzips' at the tip of a crack, where stresses are concentrated. Direct studies of the so-called small-scale yielding zone, where deformation is large, are sparing. Using hydrogels as a model brittle solid, we probe the small-scale yielding region with a combination of microscopy methods that resolve the kinematics of the deformation. A zone over which most of the energy is dissipated through the loss of cohesion is identified in the immediate surroundings of the crack tip. With direct measurements, we determine the scale and structure of the process zone, and identify how the specific loss mechanisms in this hydrogel material might generalize for brittle material failure.