Andr´e-Quillen (co)Homology, Abelianization and Stabilization
... For B ∈ C, LAb(B) gives the Quillen Homology of B. Examples: C = sSets Ab(X ) = Z[X ] =⇒ LAb(X ) = Z[X ] since X is cofibrant. π∗ LAb(X ) H∗ (X ) usual homology C = T op Ab(X ) = Sp ∞ (X ) =⇒ LAb(X ) = Sp ∞ (cX ). π∗ LAb(X ) H∗ (cY ) H∗ (X ) by the Dold-Thom Theorem Maria Basterra ...
... For B ∈ C, LAb(B) gives the Quillen Homology of B. Examples: C = sSets Ab(X ) = Z[X ] =⇒ LAb(X ) = Z[X ] since X is cofibrant. π∗ LAb(X ) H∗ (X ) usual homology C = T op Ab(X ) = Sp ∞ (X ) =⇒ LAb(X ) = Sp ∞ (cX ). π∗ LAb(X ) H∗ (cY ) H∗ (X ) by the Dold-Thom Theorem Maria Basterra ...
COMPLEXES OF INJECTIVE kG-MODULES 1. Introduction Let k be
... algebra of singular cochains on the classifying space, Ddg (C ∗ (BG; k)). Namely, if G is a p-group then there is an equivalence of categories K(Inj kG) ' Ddg (C ∗ (BG; k)). We prove that the tensor product over k of complexes in K(Inj kG) corresponds under this equivalence to the left derived tenso ...
... algebra of singular cochains on the classifying space, Ddg (C ∗ (BG; k)). Namely, if G is a p-group then there is an equivalence of categories K(Inj kG) ' Ddg (C ∗ (BG; k)). We prove that the tensor product over k of complexes in K(Inj kG) corresponds under this equivalence to the left derived tenso ...
The Theory of Polynomial Functors
... be needed so as to properly understand the functors), to see how they fit into Professor Roby’s framework of strict polynomial maps (Chapter 5). 3:o. To conduct a survey of numerical rings (in order to understand the maps). This has, admittedly, been done before, in a somewhat diverent guise, but ou ...
... be needed so as to properly understand the functors), to see how they fit into Professor Roby’s framework of strict polynomial maps (Chapter 5). 3:o. To conduct a survey of numerical rings (in order to understand the maps). This has, admittedly, been done before, in a somewhat diverent guise, but ou ...
