From 8c1054256a4ef67f109cc6d30f3d3bd050e936cb Mon Sep 17 00:00:00 2001 From: partowp Date: Mon, 3 Aug 2026 20:34:08 +0100 Subject: [PATCH] minor --- draft/draft.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/draft/draft.tex b/draft/draft.tex index e1f0014..996180d 100644 --- a/draft/draft.tex +++ b/draft/draft.tex @@ -581,9 +581,9 @@ The definition derives the ordering on morphisms of each hom-set $\Hom(X,\sub Y) \begin{align*} \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_{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} \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 Sg(\mu)(y)&(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)(y)\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)\\ \leq& 1 \end{align*}