I am unable to find an example illustrating the appropriate content that should be included within this file to localize the function category name
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It depends on the structure of the function you are implementing...
In appian-plugin.xml the following lines must be added.
<appian-plugin name="<FunctionsProjectName>" key="<package>">
<plugin-info>
<description>Description</description>
<vendor name="xxxxxxx" url="https://www.xxxxxxx.com" />
<version>1.0.0</version>
<application-version min="16.2" />
</plugin-info>
<function key="<functionKey>" class="<mainClassWithPackage>"/>
</appian-plugin>
And in properties file (<functionKey>_en_US.properties for example.),
function.<functionKey>.description=Description
function.<functionKey>.param.<paramName>.description=PArameter Description
It's described here: docs.appian.com/.../Custom_Function_Plug-ins.html
This example for the internationalization of the function itself, not for the function @Category
<function-category key="categoryFunctions" name="categoryFunctions" />