• Corpus ID: 243985985

# 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…

## References

SHOWING 1-10 OF 54 REFERENCES
The cobar construction as an $E_{\infty}$-bialgebra model of the based loop space
• Mathematics
• 2021
In the fifties, Adams introduced a comparison map θZ : ΩS (Z, z) → S (Ωz Z) from his cobar construction on the (simplicial) singular chains of a pointed space (Z, z) to the cubical singular chains on
On the multisimplicial cup product
• Mathematics
• 2020
We define a cup product on the cochain complex of a multisimplicial set, that is compatible with the classical cup product on the cochain complex of the diagonal simplicial set via the
Cochain level May–Steenrod operations
• Mathematics
Forum Mathematicum
• 2021
Abstract Steenrod defined in 1947 the Steenrod squares on the mod 2 cohomology of spaces using explicit cochain formulae for the cup-i products; a family of coherent homotopies derived from the
A cochain level proof of Adem relations in the mod 2 Steenrod algebra
• Mathematics
Journal of Homotopy and Related Structures
• 2021
In 1947, N.E. Steenrod defined the Steenrod Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup-i products of cocycles. He later recast the construction in more
Explicit symmetric DGLA models of 3-cells
• Mathematics
Abstract We give explicit formulae for differential graded Lie algebra (DGLA) models of $3$ -cells. In particular, for a cube and an $n$ -faceted banana-shaped $3$ -cell with two vertices, $n$
We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift