multidimensional-map.ps1

# names of the dimensions in the order that we take the cross product
$crossProductOrder = "Category1", "Category2", "Category3"

# get the object's identity vector, as member of the cross product
function Get-Vector([psobject] $obj) {
  $crossProductOrder | % {$obj.$_}
}

# get the path to the object in the file system
function Get-VectorPath([psobject] $obj) {
  (Get-Vector $obj) -join "/"
}

# get the values at the intersection of the sets defined by `$vector`
$vector = "category1value", "category2value", "category3value"
$vectorPath = "$container/$($vector -join "/").json"
Get-Content $vectorPath | ConvertTo-Json

# set the object
$obj | ConvertTo-Json | Out-File (Get-VectorPath $obj)