f3c974521ba0
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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,7insertions(+),7deletions(-) 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 \(\tilde{F}((\_, \mathbf{o})) = F\).