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\begin{document}

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\section*{Rainer Vogt}

\textbf{Rainer Vogt} (1942--2015) was a mathematician specialised in [[homotopy theory]].

\begin{itemize}%
\item \href{https://www.genealogy.math.ndsu.nodak.edu/id.php?id=86037}{Mathematics Genealogy page}


\item  at his former  in Osnabr\"u{}ck.


\item Rainer Vogt, \emph{My time as Mike Boardman's student and our work on infinite loop spaces} ([[VogtMemory.pdf:file]])



\end{itemize}
He received his Ph.D. from the University of Warwick and his thesis advisor was [[Michael Boardman]]. He was a a full professor at Osnabr\"u{}ck University in Germany.

He coauthored with Boardman the famous book \textbf{Homotopy invariant algebraic structures on topological spaces}, Springer Lecture Notes in Math 347 (1973).

This book introduced the notion of [[weak Kan complex]] that was later popularized by [[André Joyal]] under the name [[quasi-category]] as a natural basis for the [[higher category theory]] of [[(∞,1)-category|(∞,1)-categories]].

An early application of the ideas from that book was in the proof of what is sometimes refereed to as Vogt's theorem on categories of homotopy coherent maps, between homotopy coherent diagrams. This is briefly discussed at [[homotopy coherent diagram]]. It occurs in his paper

\begin{itemize}%
\item R.M. Vogt, \emph{Homotopy limits and colimits}, Math. Z., 134 (1973) 11-52,

\end{itemize}
which gave a neat explicit construction/description of [[homotopy limit]]s.

\hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries}

\begin{itemize}%
\item [[stable homotopy category]], [[smash product of spectra]]


\item [[quasi-category]]


\item [[Boardman-Vogt resolution]]


\item [[Boardman-Vogt tensor product]]



\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

Some of the above material is taken from [[joyalscatlab:Vogt, Rainer|Joyal's CatLab -- Rainer Vogt]].

category:people

[[!redirects Vogt, Rainer ]] [[!redirects Vogt]] [[!redirects R. Vogt]] [[!redirects R. M. Vogt]]



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