Please chceck attached file.
If I choose Category - Furniture I would like to see workbook with map. In any other case (filter=Office Supplies or Technology) I would like to see workbook with bar charts. I wanted to use "Control visibility using calue" option so I created parameter and 2 calculated fields. But I do not want user to see this parameter. User will see only filter and can choose one of three options. Is it possible to create something like that? Parameter should be changed by filter.
A parameter cannot be changed by selecting something from a normal filter. If the category is on your chart then you can set the parameter based on clicking a chart item, but you don't have that. You also need to be aware that DZV (using "Control visibility using") is calculated at the workbook level, so any filters you have applied are not used, so if you were to try to control visiblity with a field like [Category] = "Furniture", at the workbook level this can be both true and false, so Tableau will not allow you to choose it as a value to control the visibility.
You could consider having a worksheet that acted as the trigger for changing the parameter.
You can take that further and build a worksheet that looks like radio buttons, if you want. Parameters don't need to be displayed on your dashboard, so that part is easy. I've created a simple version of what I've said in your workbook. Click on the categories in the top right to change the parameter (which I've removed from the dashboard).