Commit 439a60a7 by Leonard Guetta

### edited a few typos in chapter 2. Did not yet do what said in previous commit

parent 2ac942db
 ... ... @@ -44,7 +44,7 @@ is poorly behaved. For example, \fi \gamma^* : \underline{\Hom}(\ho(\C),\D) \to \underline{\Hom}(\C,\D) \] is fully faithful and its essential image consists of functors $F~:~\C~\to~\D$ that sends morphism of $\W$ to isomorphisms of $\D$. that sends the morphisms of $\W$ to isomorphisms of $\D$. We shall always consider that $\C$ and $\ho(\C)$ have the same class of objects and implicitly use the equality ... ... @@ -90,7 +90,7 @@ For later reference, we put here the following definition. is commutative. Let $G : (\C,\W) \to (\C',\W')$ be another morphism of localizers. A \emph{$2$\nbd{}morphism of localizers} from $F$ to $G$ is simply a natural transformation $\alpha : F \Rightarrow G$. The universal property of the localization implies that there exists a canonical natural transformation the localization implies that there exists a unique natural transformation \[ \begin{tikzcd} \ho(\C) \ar[r,bend left,"\overline{F}",""{name=A,below}] \ar[r,bend right,"\overline{G}"',""{name=B,above}] & \ho(\C') ... ... @@ -109,8 +109,8 @@ For later reference, we put here the following definition. \end{paragr} \begin{remark}\label{remark:localizedfunctorobjects} Since we always consider that for every localizer $(\C,\W)$ the categories $\C$ and $\ho(\C)$ have the same objects and the localization functor is the identity on objects, it follows that for a morphism of localizer ${F : (\C,\W) and$\ho(\C)$have the same class of objects and the localization functor is the identity on objects, it follows that for a morphism of localizers${F : (\C,\W) \to (\C',\W')}\$, we tautologically have \[ \overline{F}(X)=F(X) ... ...
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