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 $\star \colon \mathbb{M}(V)\otimes \mathbb{L}(W)\to \mathbb{L}(V\oplus W\oplus s(V\otimes W))$, 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 $Δ\colon X\to X\times X$.

Theorems & Definitions (46)

• Example 2.1
• Theorem 2.2
• Lemma 2.3
• Example 2.4
• Definition 2.5
• Theorem 2.6
• proof
• Definition 3.1
• Lemma 3.2
• Remark 3.3: The tree notation