The Wikipedia category graph serves as the taxonomic backbone for large-scale knowledge graphs like YAGO or Probase, and has been used extensively for tasks like entity disambiguation or semantic similarity estimation. Wikipedia's categories are a rich source of taxonomic as well as non-taxonomic information. The category 'German science fiction writers', for example, encodes the type of its resources (Writer), as well as their nationality (German) and genre (Science Fiction). Several approaches in the literature make use of fractions of this encoded information without exploiting its full potential. In this paper, we introduce an approach for the discovery of category axioms that uses information from the category network, category instances, and their lexicalisations. With DBpedia as background knowledge, we discover 703k axioms covering 502k of Wikipedia's categories and populate the DBpedia knowledge graph with additional 4.4M relation assertions and 3.3M type assertions at more than 87% and 90% precision, respectively.