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We devise a unified framework for the design of canonization algorithms.Using hereditarily finite sets, we define a general notion of combinatorialobjects that includes graphs, hypergraphs, relational structures, codes,permutation groups, tree decompositions, and so on.  Our approach allows for a systematic transfer of the techniques that havebeen developed for isomorphism testing to canonization. We use it to design acanonization algorithm for combinatorial objects in general. This result givesnew fastest canonization algorithms with an asymptotic running time matchingthe best known isomorphism algorithm for the following types of objects:hypergraphs, hypergraphs of bounded color class size, permutation groups (up topermutational isomorphism) and codes that are explicitly given (up to codeequivalence).

A unifying method for the design of algorithms canonizing combinatorial objects