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This paper relates how a "simple" result in combinatorial homotopy eventually led to a totally new understanding of basic theorems in Algebraic Topology, namely the Eilenberg-Zilber theorem, the twisted Eilenberg-Zilber theorem, and finally the Eilenberg-MacLane correspondance between the Classifying Space and Bar constructions. In the last case, it was an amazing lucky consequence of computations based on conjectures not yet proved. The key new tool used in this context is Robin Forman'sdoi:10.1145/2442829.2442871 dblp:conf/issac/RomeroS12 fatcat:ie2rzslscfacpgndmjkloswz4a