Geodesic
Combinatorial Route to Algebra: The Art of Composition Decomposition
Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2.

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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 choice thereof. It will be demonstrated how this leads to multiplication and co-multiplication laws, thereby providing a generic scheme furnishing combinatorial classes with an algebraic structure. The paper is meant as a gentle introduction to the concepts of composition and decomposition with the emphasis on combinatorial origin of the ensuing algebraic constructions. 
@article{DMTCS_2010_12_2_a2,
     author = {Blasiak, Pawel},
     title = {Combinatorial {Route} to {Algebra:} {The} {Art} of {Composition} & {Decomposition}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2010},
     doi = {10.46298/dmtcs.481},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.481/}
}
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Blasiak, Pawel. Combinatorial Route to Algebra: The Art of Composition & Decomposition. Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2. doi : 10.46298/dmtcs.481. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.481/

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