namely universal properties (in the sense of category theory). In particular, partial map classifiers in the topos of graphs (and its slice categories) cover the purely structural aspects of materializations; this is related to final pullback complements [@DT87], a fundamental construction of graph rewriting [@l:graph-rewritinginspancat; @chhk:sesqui]. Annotations of shape graphs are treated orthogonally via op-fibrations. The first milestones of a general framework for shape analysis of graph transformation and more generally rewriting of objects in a topos are the following: [${\rhd}$]{} A rewriting formalism for graph abstractions that lifts the rule-based rewriting from single graphs to *abstract graphs*; it is developed for (abstract) objects in a topos. [${\rhd}$]{} We characterize the materialization operation for abstract objects in a topos in terms of partial map classifiers, giving a sound and complete description of all occurrences of right-hand sides of rules obtained by rewriting an abstract object. [${\rhd}$]{} We decorate abstract objects with annotations from an ordered monoid and extend abstract rewriting to abstract objects with annotations. For the specific case of graphs, we consider global annotations (counting the nodes and edges in a graph), local annotations (constraining the degree of a node), and path annotations (constraining the existence of paths between 