f3c974521ba0 — Benedikt Fluhr <http://bfluhr.com> 5 years ago
Change of Terminology: D-category instead of D-module

We use the term D-category where we previously used the term D-module
to avoid a clash of terminology,
since D-modules already exist and are something completely different.
This has been pointed out by Michael Catanzaro.
1 files changed, 7 insertions(+), 7 deletions(-)

M poster.tex
M poster.tex +7 -7
@@ 198,15 198,15 @@ 
     for all \((a, b; c, d) \in \mathcal{D}\).
   }
   \column{0.5}
-  \block{Interleavings in \(D\)-modules}{
-    \begin{definition}[\(D\)-modules]
-      A \emph{\(D\)-module} is a category \(\mathcal{C}\)
+  \block{Interleavings in \(D\)-categories}{
+    \begin{definition}[\(D\)-categories]
+      A \emph{\(D\)-category} is a category \(\mathcal{C}\)
       with a strict monoidal functor \(\mathcal{S}\) from \(D\)
       to the category of endofunctors on \(\mathcal{C}\).
       We refer to \(\mathcal{S}\) as the
       \emph{smoothing functor of \(\mathcal{C}\)}.
     \end{definition}
-    Now let \(\mathcal{C}\) be a \(D\)-module
+    Now let \(\mathcal{C}\) be a \(D\)-category
     with smoothing functor \(\mathcal{S}\).
     For \(a \leq 0\), \(b \geq 0\), and an object \(A\) in \(\mathcal{C}\)
     we get two things,

          
@@ 273,10 273,10 @@ 
       and \(\mu(A, B)\) the
       \emph{relative interleaving distance}.
     \end{definition}
-    Now let \(\mathcal{C}'\) be another \(D\)-module with smoothing
+    Now let \(\mathcal{C}'\) be another \(D\)-category with smoothing
     functor \(\mathcal{S}'\).
     \begin{definition}
-      A \(1\)-homomorphism of \(D\)-modules
+      A \(1\)-homomorphism of \(D\)-categories
       from \(\mathcal{C}\) to \(\mathcal{C}'\)
       is a functor from \(\mathcal{C}\) to \(\mathcal{C}'\) such that
       \[

          
@@ 337,7 337,7 @@ 
     to a category \(\mathcal{C}\).
     \begin{definition}
       A \emph{persistence-enhancement of \(F\)}
-      is the structure of a \(D\)-module on \(\mathcal{C}\)
+      is the structure of a \(D\)-category on \(\mathcal{C}\)
       together with a \(1\)-homomorphism \(\tilde{F}\) from
       \(\mathcal{F}\) to \(\mathcal{C}\) such that
       \(\tilde{F}((\_, \mathbf{o})) = F\).