Homology, Homotopy and Applications
Volume 14 (2012)
Cubical approach to derived functors
Pages: 133 – 158
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