What is a cone of a lattice?

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I'm reading Fulton Harris group representation theory. I encountered this:

"The virtual characters of $G$ form a lattice $\Lambda \cong \mathbb Z^{\mathfrak c} \in \mathbb C_{\text{class}}(G)$, in which the actual characters sit as a cone $\Lambda_0 \cong \mathbb N^{\mathfrak c} \subset \mathbb Z^{\mathfrak c}$"

I've only ever taken an introduction to Lattice theory, when I took abstract algebra, and I don't think I've encountered the term "cone", and when searching for what a cone of a lattice is, the results are confusing and I can't make sense of them.