Tag Archives: homotopy

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 […]