Homology, Homotopy and Applications

Volume 14 (2012)

Number 1

Cubical approach to derived functors

Pages: 133 – 158

DOI: http://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

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