The category of punctual strictly $K$-analytic spaces is the following: The objects are pairs $(X,x)$ where $X$ is a strictly $K$-analytic space and $x\in X$ is a point. A morphism $\varphi:(X,x)\rightarrow(Y,y)$ is a morphism $\varphi:X\rightarrow Y$ of strictly $K$-analytic spaces such that $\varphi(x)=y$.

The category $(K\textrm{-Germs})$ of germs of a strictly $K$-analytic space at a point is defined to be the localization of the category of punctual strictly $K$-analytic spaces by the system of morphisms $\varphi:(X,x)\rightarrow(Y,y)$ which identify $X$ with an open neighbourhood of $y$ in $Y$. The germ induced by the punctual strictly $K$-analytic space $(X,x)$ is denoted by $X_{x}$.

A germ $X_{x}$ is said to be good if $x$ has a strictly $K$-affinoid neighbourhood in $X$. A morphism of germs $\varphi:X_{x}\rightarrow Y_{y}$ is said to be separated resp. closed if it is induced by a separated resp. boundaryless morphism $X^{\prime}\rightarrow Y$ for an open neighbourhood $X^{\prime}$ of $x$ in $X$ (recall that a morphism $\varphi:X\rightarrow Y$ of $K$-analytic spaces is called boundaryless if $X=\Int(X/Y)$, where the relative interior $\Int(X/Y)$ is defined to be the set of all $x\in X$ such that for any affinoid domain $V\subseteq Y$ with $\varphi(x)\in V$ there is an affinoid neighbourhood $U\subseteq\varphi^{-1}(V)$ of $x$ in $\varphi^{-1}(V)$ such that $x\in\Int(U/V)$).