Cyclic homology, comodules, and mixed complexes

Hochschild and cyclic homology of finite type algebras

“…Lemma 5 can be used to identify some subquotients of the filtration (17). We shall use the notation of Definition 4.…”

Homotopy of planar Lie group equivariant presheaves

“…What can be said is that in the weak model case, Dwyer and Kan proved that the category of R-modules equipped with the weak model is Quillen equivalent to another category, namely the category of mixed complexes [8]. And then in [19] Kassel shows that there is a way to compute cyclic cohomology as derived functors on a mixed complex using an Ext construction. Therefore, we see that in the weak cyclic case, we retrieve a cyclic cohomology, which can be seen as a Borel type equivariant cohomology theory as shown in [18].…”

Differential graded categories

“…2] to a mixed complex C(A) in the sense of [72], i.e. a dg module over the dg algebra Λ = k[B]/(B 2 ), where B is of degree −1 and dB = 0.…”

“…a dg module over the dg algebra Λ = k[B]/(B 2 ), where B is of degree −1 and dB = 0. As shown in [72], all variants of cyclic homology [100] only depend on C(A) considered in D(Λ). For example, the cyclic homology of A is the homology of the complex C(A) L ⊗ Λ k. If A is a k-flat differential graded category, its mixed complex is the sum-total complex of the bicomplex obtained as the natural re-interpretation of the above complex.…”