Explicit Quillen models for Cartesian products of $2$-cones

Abstract

We give an explicit minimal Quillen model for the Cartesian product $X\times Y$ of rational $2$-cones in terms of derivations and a binary operation $\star :\mathbb{M}(V)\otimes \mathbb{L}(W)\to \mathbb{L}(V\oplus W\oplus s(V\otimes W))$, where $(\mathbb{L}(V),\partial )$ and $(\mathbb{L}(W),\partial )$ are Quillen minimal models for $X$ and $Y$ respectively and $\mathbb{M}$ denotes the free magma on $W$. The model presented also allows us to explicitly describe a model for the diagonal map $\Delta :X\to X\times X$.

28 pages