Homology, Homotopy and Applications

Volume 14 (2012)

Number 1

Cubical approach to derived functors

Pages: 133 – 158

DOI: https://dx.doi.org/10.4310/HHA.2012.v14.n1.a7


Irakli Patchkoria (Mathematisches Institut, Universität Bonn, Germany)


We construct a cubical analog of the Tierney-Vogel theory of simplicial derived functors and prove that these cubical derived functors are naturally isomorphic to their simplicial counterparts. We also show that this result generalizes the well-known fact that the simplicial and cubical singular homologies of a topological space are naturally isomorphic.


derived functor, normalized chain complex, presimplicial object, projective class, projective pseudocubical resolution, pseudocubical object

2010 Mathematics Subject Classification

18E25, 18G10, 18G25, 18G30, 55N10

Published 13 July 2012