group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
algebraic topology – application of higher algebra and higher category theory to the study of (stable) homotopy theory
geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
Waldhausen’s A-theory (Waldhausen 85) of a connected homotopy type $X$ is the algebraic K-theory of the suspension spectrum $\Sigma^\infty_+ (\Omega X)$ of the loop space $\Omega X$, hence of the ∞-group ∞-rings $\mathbb{S}[\Omega X]$ of the looping ∞-group $\Omega X$, hence the K-theory of the parametrized spectra over $X$ (Hess-Shipley 14).
The definition is originally due to
The interpretation in terms of certain module spectra over the Spanier-Whitehead dual of $X$ is due to
and the interpretation in terms of $\mathbb{S}[\Omega X]$-module spectra and Koszul dually in terms of $\mathbb{S}[X]$-comodule spectra (using the canonical coring spectrum-structure of suspension spectra) is due to:
Last revised on August 21, 2022 at 14:28:20. See the history of this page for a list of all contributions to it.