pouya/coalgebraic-simulation
2
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

minor

Browse Source
This commit is contained in:
partowp
2026-08-03 20:34:08 +01:00
parent 51b64cc427
commit 8c1054256a
1 changed files with 3 additions and 3 deletions
Download Patch File Download Diff File Expand all files Collapse all files
draft/draft.tex
+3 -3
View File
@@ -581,9 +581,9 @@ The definition derives the ordering on morphisms of each hom-set $\Hom(X,\sub Y)
\begin{align*} \begin{align*}
\sum_{x \in X} \mu'(x)&\\ \sum_{x \in X} \mu'(x)&\\
=& \sum_{x \in X} \frac{\nu(g(x))}{Sg(\mu)(g(x))} \comp \mu(x)&(Sg(\mu)(g(x))\neq 0)\\ =& \sum_{x \in X} \frac{\nu(g(x))}{Sg(\mu)(g(x))} \comp \mu(x)&(Sg(\mu)(g(x))\neq 0)\\
=& \sum_{y \in Y} \sum_{x \in g^{\mone}(y)} \frac{\nu(y)}{Sg(\mu)(y)} \comp \mu(x)&(Sg(\mu)(g(x))\neq 0)\\ =& \sum_{y \in Y} \sum_{x \in g^{\mone}(y)} \frac{\nu(y)}{Sg(\mu)(y)} \comp \mu(x)&(Sg(\mu)(y)\neq 0)\\
=& \sum_{y \in Y} \frac{\nu(y)}{Sg(\mu)(y)} \comp \sum_{x \in g^{\mone}(y)} \mu(x)&(Sg(\mu)(g(x))\neq 0)\\ =& \sum_{y \in Y} \frac{\nu(y)}{Sg(\mu)(y)} \comp \sum_{x \in g^{\mone}(y)} \mu(x)&(Sg(\mu)(y)\neq 0)\\
=& \sum_{y \in Y} \frac{\nu(y)}{Sg(\mu)(y)} \comp Sg(\mu)(y)&(Sg(\mu)(g(x))\neq 0)\\ =& \sum_{y \in Y} \frac{\nu(y)}{Sg(\mu)(y)} \comp Sg(\mu)(y)&(Sg(\mu)(y)\neq 0)\\
=& \sum_{y \in Y} \nu(y)\\ =& \sum_{y \in Y} \nu(y)\\
\leq& 1 \leq& 1
\end{align*} \end{align*}