Menu lists acting as filters of another list

filtri

like this, where the first horizontal menu list of filters is the father of the second horizontal list of filters, and maybe there will be a 3rd one and on the bottom the vertical list is the filtered one, maybe updating as the filters get selected.
Also, some method to make it more elegant, like instead of more than one horizontal filter to have just one that updates as the user clicks, but in that case there must be some button or something that allows to go back