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extract-category ket
extract the "category" from the given ket
categories are separated by ": "
with the most general category on the left, and the most specific on the right
for example |animal: mammal: dog>
has the most general category "animal", then the category "mammal" and then finally the "value" dog
categories can be considered a type for the object
Eg, |word: house> says house is a type of word
and |food: apple> says apple is a type of food
and we can define operators with respect to them
Eg, op |food: *> #=> ...
will define "op" with respect to all objects of type\category "food".

-- if there is no category, then return the empty ket:
-- NB: this is in contrast to the python version of the Semantic DB which would instead return |dog>
extract-category |dog>
    |>

-- remove the "value" from the ket:
-- in other words, extract the category of the ket
extract-category |animal: mammal: dog>
    |animal: mammal>

-- remove the "value" from the ket, and then the most specific "category":
extract-category extract-category |animal: mammal: dog>
    |animal>

-- or using the powered-operator notation:
extract-category^2 |animal: mammal: dog>
    |animal>

-- an abstract example:
extract-category |a: b: c: d: e: f>
    |a: b: c: d: e>