The Stacks project

Definition 4.6.2. We say a commutative diagram

\[ \xymatrix{ w \ar[r] \ar[d] & z \ar[d] \\ x \ar[r] & y } \]

in a category is cartesian if $w$ and the morphisms $w \to x$ and $w \to z$ form a fibre product of the morphisms $x \to y$ and $z \to y$.

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View Definition 4.6.2 as pdf