My question is about a small detail on page 132 of the above-mentioned book.

Let $R'$ be a faithfully flat $R$ algebra and $M'$ a $R'$-module. Let $\varphi: p_1^* M' \cong p_2^* M'$ be a covering datum, where $p_1$ and $p_2$ are projections onto the first and second factor from $R'' = R'\otimes_{R} R'$ to $R'$ (or rather, projection of the associated spectra). Using $\varphi$, the book derives two morphisms $$M' \rightrightarrows M'\otimes_R R' $$ and say that this is co-cartesian over $$ R' \rightrightarrows R'\otimes_R R'.$$ It's also said there that being co-cartesian over the second sequence is equivalent to giving a covering datum.

Next, they talk about descent datum (covering datum plus some co-cycle condition), relating descent datum with some diagram with triple arrows being co-cartesian over a similar sequence on the rings (involving $R'\otimes_R R' \otimes_R R'$). They then make a similar remark as above: descent datum = co-cartesian + some commutativity conditions such as eg. $p_1\circ p_{12} = p_1 \circ p_{13}$.

I don't quite understand what they mean by being co-cartesian. And so, I also don't see how it's related to giving a descent or descent datum. It would be helpful if someone can clarify.

Thanks!

EDIT: I started reading the relevant section in the Stacks project. They use the formalism of cosimplicial object, which makes everything much clearer.