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We consider a general concept of composition and decomposition of objects,and discuss a few natural properties one may expect from a reasonable choicethereof. It will be demonstrated how this leads to multiplication and co-multiplication laws, thereby providing a generic scheme furnishingcombinatorial classes with an algebraic structure. The paper is meant as agentle introduction to the concepts of composition and decomposition with theemphasis on combinatorial origin of the ensuing algebraic constructions.

Combinatorial Route to Algebra: The Art of Composition & Decomposition