Il faut que je finisse de nettoyer la section 5.3 (à partir de corollaire 5.3.9)

hmlgy.tex

@@ -138,7 +138,7 @@ We write $\Ab$ for category of abelian groups and for an abelian group $G$, we w
 \begin{proof}
   The category of chain complexes is equivalent to the category $\omega\Cat(\Ab)$ of $\omega$-categories internal to abelian groups (see \cite[Theorem 3.3]{bourn1990another}) and with this identification, the functor $\lambda : \omega\Cat \to \omega\Cat(\Ab)$ is nothing but the left adjoint of the canonical forgetful functor $\omega\Cat(\Ab) \to \omega\Cat$.
 \end{proof}
-As we shall now see, when the $\oo$\nbd-categoru $C$ is \emph{free} the chain complex $\lambda(C)$ admits a nice expression.
+As we shall now see, when the $\oo$\nbd-category $C$ is \emph{free} the chain complex $\lambda(C)$ admits a nice expression.
 \begin{paragr}
   Let $n\geq 0$. Recall that for every monoid $M$ (supposed commutative if $n \geq 1$) we have defined in Section \ref{sec:suspmonoids} an $n$\nbd-category $B^nM$ whose set of $n$\nbd-cells is isomorphic to the underlying set of $M$. And the correspondence $M \mapsto B^nM$ defines a functor in the expected way. By considering abelian groups as particular cases of (commutative) monoids, we obtain a functor for each $n\geq 0$ 
   \begin{align*}

homtheo.tex

@@ -701,7 +701,7 @@ We now turn to the most important way of obtaining op-prederivators.
   \begin{proof}
     See for example \cite[Proposition 3.4]{cisinski2003images}.
   \end{proof}
-  \begin{paragr}
+  \begin{paragr}\label{paragr:projmod}
     The model structure of the previous proposition is referred to as the \emph{projective model structure on $\M(A)$}.
   \end{paragr}
   \begin{proposition}
@@ -725,7 +725,7 @@ By definition of the projective model structure, $u^*$ preserve weak equivalence
       \]
       is a Quillen adjunction. Since $\hocolim_A$ is the left derived of $\colim_A$, we have the following immediate corollary of the previous proposition.
     \end{paragr}
-    \begin{corollary}
+    \begin{corollary}\label{cor:cofprojms}
       Let $(\M,\W,\Cof,\Fib)$ be a cofibrantely generated model category, $A$ a small category and $X : A \to \M$ a diagram. If $X$ is cofibrant for the projective model structure on $\C(A)$, then the canonical morphism of $\ho(\C)$
       \[
       \hocolim_A(X) \to \colim_A(X)
@@ -741,7 +741,7 @@ By definition of the projective model structure, $u^*$ preserve weak equivalence
     \end{proof}
 
     Below is a particular case for which the previous corollary applies.
-    \begin{proposition}
+    \begin{proposition}\label{prop:sequentialhmtpycolimit}
       Let $(\M,\W,\Cof,\Fib)$ be a cofibrantely generated model category and let $X$ be a sequential diagram in $\M$
       \[
       X_0 \to X_1 \to X_2 \to \cdots
@@ -753,7 +753,7 @@ By definition of the projective model structure, $u^*$ preserve weak equivalence
     \end{proof}
     Another setting for which a category of diagrams $\M(A)$ can be equipped with a model structure whose weak equivalences are pointwise equivalences and for which the $A$-colimit functor is left Quillen is when the category $A$ is a \emph{Reedy category}. Rather that recalling this theory, we simply put here the only practical result that we shall need in the sequel.
     
-    \begin{lemma}\label{lemma:hmptycocartesianreedy}
+    \begin{lemma}\label{lemma:hmtpycocartesianreedy}
       Let $(\M,\W,\Cof,\Fib)$ be a model category and let
       \[
       \begin{tikzcd}

omegacat.tex

@@ -1071,7 +1071,7 @@ We can now prove the expected result.
     \todo{À finir ? Il faudrait peut-être dire qu'en rajoutant des hypothèses on doit pouvoir quand même avoir une forme normale. Dans le cas n=2, quand on fait l'hypothèse que le 2-polygraphe est positif, je sais que c'est vrai.}
   \end{paragr}
  
-  \section{Discrete Conduché $\oo$-functors}
+  \section{Discrete Conduché $\oo$-functors}\label{section:conduche}
 
   \begin{paragr}
     Recall that given a category $\C$ and a class $M$ of arrows of $\C$, we say that an arrow $f : X \to Y$ of $\C$ is \emph{left orthogonal} to $M$ if for every $m : A \to B$ in $M$ and every solid arrow square
@@ -1135,7 +1135,7 @@ We can now prove the expected result.
    means exactly that $x=1^{n}_y$.
     \end{paragr}
   \begin{definition}\label{def:conduche}
-    An $\oo$-functor $F : C \to D$ is an \emph{discrete Conduché $\oo$-functor} if it is right orthogonal to the $\oo$-functors
+    An $\oo$-functor $F : C \to D$ is an \emph{discrete Conduché $\oo$\nbd-functor} if it is right orthogonal to the $\oo$-functors
         \[
    \kappa^n_k : \sD_n \to \sD_k
    \]