Small fixes

Thanks to Keenan Kidwell
http://stacks.math.columbia.edu/tag/0164#comment-253
http://stacks.math.columbia.edu/tag/0164#comment-254
http://stacks.math.columbia.edu/tag/016I#comment-255
http://stacks.math.columbia.edu/tag/05AY#comment-256

descent.tex

@@ -1715,7 +1715,7 @@ \section{Descent of finiteness properties of modules}
 Let $X$ be a scheme.
 Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_X$-module.
 Let $\{f_i : X_i \to X\}_{i \in I}$ be an fpqc covering such that
-each $f_i^*\mathcal{F}$ is locally generate by $r$ sections as an
+each $f_i^*\mathcal{F}$ is locally generated by $r$ sections as an
 $\mathcal{O}_{X_i}$-module. Then $\mathcal{F}$ is locally generated by
 $r$ sections as an $\mathcal{O}_X$-module.
 \end{lemma}

simplicial.tex

@@ -33,9 +33,9 @@ \section{The category of finite ordered sets}
 \begin{enumerate}
 \item objects $[0], [1], [2], \ldots$ with
 $[n] = \{0, 1, 2, \ldots, n\}$ and
-\item a morphism $[n] \to [m]$ is the set of nondecreasing
-maps of the corresponding
-sets $\{0, 1, 2, \ldots, n\} \to \{0, 1, 2, \ldots, m\}$.
+\item a morphism $[n] \to [m]$ is a nondecreasing map
+$\{0, 1, 2, \ldots, n\} \to \{0, 1, 2, \ldots, m\}$
+between the corresponding sets.
 \end{enumerate}
 Here {\it nondecreasing} for a map $\varphi : [n] \to [m]$
 means by definition that $\varphi(i) \geq \varphi(j)$ if $i \geq j$.
@@ -60,7 +60,7 @@ \section{The category of finite ordered sets}
 \begin{lemma}
 \label{lemma-face-degeneracy}
 Any morphism in $\Delta$ can be written as a composition
-of an identity morphism, and the morphisms $\delta^n_j$ and $\sigma^n_j$.
+of the morphisms $\delta^n_j$ and $\sigma^n_j$.
 \end{lemma}
 
 \begin{proof}
@@ -421,7 +421,7 @@ \section{Cosimplicial objects}
 $\delta^n_j$, $\sigma^n_j$ satisfying these relations there exists a unique
 cosimplicial object $U$ in $\mathcal{C}$ such that $U_n = U([n])$,
 $\delta^n_j = U(\delta^n_j)$, and $\sigma^n_j = U(\sigma^n_j)$.
-\item A morphism between simplicial objects $U$ and $U'$
+\item A morphism between cosimplicial objects $U$ and $U'$
 is given by a family of morphisms $U_n \to U'_n$ commuting
 with the morphisms $\delta^n_j$ and $\sigma^n_j$.
 \end{enumerate}