# The diagonal of cellular spaces and effective algebro-homotopical constructions

@inproceedings{MedinaMardones2021TheDO, title={The diagonal of cellular spaces and effective algebro-homotopical constructions}, author={Anibal M. Medina-Mardones}, year={2021} }

. In this survey article we discuss certain homotopy coherent en- hancements of the coalgebra structure on cellular chains deﬁned by an approximation to the diagonal. Over the rational numbers, C ∞ -coalgebra structures control the Q -complete homotopy theory of spaces, and over the integers, E ∞ coalgebras provide an appropriate setting to model the full homotopy category. Eﬀective constructions of these structures, the focus of this work, carry geometric and combinatorial information which…

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