@@ 1,4 1,4 @@ 
-# Extended Persistence Enhancements
+# Complete Persistence Enhancements
 
 In the previous section we defined positive persistence enhancements
 of functor on $\R$-spaces and provided one for $\mathcal{C}$,

          
@@ 121,7 121,6 @@ with the interleavings of $A$ and $B$ wi
 
 Homomorphisms of $-D$- and $\Ec$-categories are defined completely
 analogously to those of $D$-categories.
-Now we provide a negative and extended version of $\mathbf{F}$.
 
 * **Definition.**
 Here we define the categories $-\mathbf{F}$ and $\pm \mathbf{F}$.

          
@@ 143,12 142,12 @@ Whenever there is any ambiguity interpre
 of this inequality, we interpret it as $-\infty$, for the right-hand side
 as $\infty$.
 
-Next we define negative and extended persistence-enhancements.
+Next we define negative and complete persistence-enhancements.
 To this end let $F$ be a functor from the category of $\R$-spaces
 to some category $\mathbf{C}$.
 
 * **Definition.**
-A *negative* respectively a *extended persistence-enhancement of $F$*
+A *negative* respectively a *complete persistence-enhancement of $F$*
 is the structure of a strict $-D$-category respectively $\Ec$-category on
 $\mathbf{C}$ together with a $1$-homomorphism $\tilde{F}$ from
 $-\mathbf{F}$ resepctively $\pm \mathbf{F}$

          

@@ 292,7 292,7 @@ we gave the category of set-valued preco
 $\overline{\R}_{-\infty}$
 the structure of an $\Ec$-category.
 So by lemma @pmDEquiv, from the section on
-[extended persistence enhancements][],
+[complete persistence enhancements][],
 the interleavings of
 $\mathcal{C} \mathcal{E} f$ and $\mathcal{C} \mathcal{E} g$
 with respect to the $-D$-category structure given by