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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 10th 2015
• (edited Nov 10th 2015)

I have (finally) added some pointers to the result of Freed-Hopkins 13 to relevant $n$Lab entries.

pointing out that this adds further rationalization to the construction of connections on principal infinity-bundles – via Lie integration.

In making these edits, I have created and then used a little table-for-inclusion

Presently this displays as follows:

Chevalley-Eilenberg algebra CE $\leftarrow$ Weil algebra W $\leftarrow$ invariant polynomials inv

differential forms on moduli stack $\mathbf{B}G_{conn}$ of principal connections (Freed-Hopkins 13):

$\array{ CE(\mathfrak{g}) &\simeq& \Omega^\bullet_{li \atop cl}(G) \\ \uparrow && \uparrow \\ W(\mathfrak{g}) &\simeq & \Omega^\bullet(\mathbf{E}G_{conn}) & \simeq & \Omega^\bullet(\mathbf{\Omega}(-,\mathfrak{g})) \\ \uparrow && \uparrow \\ inv(\mathfrak{g}) &\simeq& \Omega^\bullet(\mathbf{B}G_{conn}) & \simeq & \Omega^\bullet(\mathbf{\Omega}(-,\mathfrak{g})/G) }$