Cross effects and calculus in an unbased setting

Abstract

We study functors $F:\mathcal {C}_f\rightarrow \mathcal {D}$ where $\mathcal {C}$ and $\mathcal {D}$ are simplicial model categories and $\mathcal {C}_f$ is the category consisting of objects that factor a fixed morphism $f:A\rightarrow B$ in $\mathcal {C}$. We define the analogs of Eilenberg and Mac Lane's cross effect functors in this context, and identify explicit adjoint pairs of functors whose associated cotriples are the diagonals of the cross effects. With this, we generalize the cotriple Taylor tower construction of

Locations

• arXiv (Cornell University) - View - PDF
• Transactions of the American Mathematical Society - View - PDF