From 9384c7ad24bd89e12f39814d667214c2dcfa063f Mon Sep 17 00:00:00 2001 From: marcbezem Date: Thu, 3 Oct 2024 14:48:30 +0200 Subject: [PATCH] minor in 5.2 --- actions.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/actions.tex b/actions.tex index 71f1bb7..b0cb654 100644 --- a/actions.tex +++ b/actions.tex @@ -176,7 +176,7 @@ \section{Group actions ($G$-sets)} \[ \Hom(H,G)(x,y)\jdeq %\Copy_{\mkgroup}((\BH_\div,x) \ptdto (\BG_\div,y)). - \Copy_{\mkgroup}(\sum_{f:\BH_\div\to \BG_\div}(y\eqto f(x))). + \Copy_{\mkgroup}\bigl(\sum_{f:\BH_\div\to \BG_\div}(y\eqto f(x))\bigr). \] Thus the type $\Hom(H,G)$ may also be considered to be a $(H\times G)$-set \[ @@ -408,7 +408,9 @@ \subsection{Actions in a type} Oftentimes it is interesting not to have an action on a set, but on an element in any given type (not necessarily the type of sets). For instance, a group can act on another, giving rise to the notion of the semidirect product in \cref{sec:Semidirect-products}. We will return these more general types of actions many times. \begin{definition}\label{action} - If $G$ is any (possibly higher) group and $A$ is any type of objects, + If $G$ is any group\footnote{% + Even an $\infty$-group in the sense of \cref{sec:inftygps}.} + and $A$ is any type of objects, then we define an \emph{action} by $G$ in %the world of elements of $A$ as a function \[