Category Archives: algebraic-topology

## Ravenel's "Nilpotence and periodicity in stable homotopy theory" Free Download

Doug Ravenel has made his book Nilpotence and periodicity in stable homotopy theory available for free download along with a list of errata, also available at the same page as the book. Here is the official description from Princeton University Press: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic […]

## A is Homotopy Equivalent to A^op via Functors

Let $\mathcal{A}$ be a small category and $\mathbf{B}\mathcal{A}$ its geometric realisation. It is evident that $\mathbf{B}\mathcal{A}$ and $\mathbf{B}\mathcal{A}^\circ$ are homotopy equivalent, and in fact homeomorphic. However, can we find functors that realise this equivalence? This post summarises some informal notes I have written on this following D. Quillen's paper Higher Algebraic […]