In their classic book, Cartan and Eilenberg described a more-or-less general scheme for defining homology and cohomology theories for a number of different kinds of algebraic structure, using a general theory of augmented algebras. Later, in his doctoral dissertation, Beck showed how to use the theory of triples to derive a very different and completely general scheme for doing the same thing. ...

We use the homological perturbation lemma to give an explicit proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f : X → BF , where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of the category of spaces over BF and corresponding strong symmetric monoidal Thom spectrum functors. Our main result identifies the topological Hochschild h...