Nonstandard definition presheaf

Thanks to Kevin Buzzard https://stacks.math.columbia.edu/tag/009I#comment-3229
stacks · May 17, 2018 · 10e8276 · 10e8276
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diff --git a/CONTRIBUTORS b/CONTRIBUTORS
@@ -27,6 +27,7 @@ Martin Bright
 David Brown
 Niels Borne
 Ragnar-Olaf Buchweitz
+Kevin Buzzard
 Jakub Byszewski
 Samir Canning
 Robert Cardona

diff --git a/sheaves.tex b/sheaves.tex
@@ -3631,6 +3631,7 @@ \section{Bases and sheaves}
 $\mathcal{F}(U)$ and to each inclusion $V \subset U$
 of elements of $\mathcal{B}$ a map
 $\rho^U_V : \mathcal{F}(U) \to \mathcal{F}(V)$ such that
+$\rho^U_U = \text{id}_{\mathcal{F}(U)}$ for all $U \in \mathcal{B}$
 whenever $W \subset V \subset U$ in $\mathcal{B}$ we have
 $\rho^U_W = \rho^V_W \circ \rho ^U_V$.
 \item A {\it morphism $\varphi : \mathcal{F} \to \mathcal{G}$