# nLab Rainer Vogt

Rainer Vogt (1942–2015) was a mathematician who specialised in homotopy theory.

He received his Ph.D. from the University of Warwick and his thesis advisor was Michael Boardman. He was a a full professor at Osnabrück University in Germany.

He coauthored with Boardman the famous book 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)-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

• R.M. Vogt, Homotopy limits and colimits, Math. Z., 134 (1973) 11-52,

which gave a neat explicit construction/description of homotopy limits.

## Selected writings

On convenient categories of topological spaces in the generality subsuming compactly generated topological spaces and Delta-generated topological spaces:

• Roland Schwänzl, Rainer Vogt, The categories of $A_\infty$- and $E_\infty$-monoids and ring spaces as closed simplicial and topological model categories, Archives of Mathematics 56 (1991) 405-411 (doi:10.1007/BF01198229)

## References

Some of the above material is taken from Joyal's CatLab – Rainer Vogt.

category: people

Last revised on October 1, 2021 at 04:55:08. See the history of this page for a list of all contributions to it.