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ReactJS can display items based on their respective categories by filtering them based on the category parameter. This can be done in several ways:

1. Using Array.filter() method: This method filters the array based on a condition and returns a new array that meets the condition. We can use it to filter items based on their category.

2. Using conditional rendering: This approach involves writing a logic to render items based on their category. We can use an if-else statement or a switch statement to render items based on their category.

3. Using ReactJS libraries: There are several ReactJS libraries that we can use to filter and display items based on their category. Some popular ones include react-filter-search and react-sortable-tree.

Overall, the approach will depend on the specific requirements of the project, but these are some common ways to display items based on their respective categories in ReactJS.