Is "Proof-of-work" a subset of "Byzantine fault tolerance (BFT)"? Can we say that Proof-of-work is a type of Byzantine fault tolerance (BFT) ? In other words, is PoW a subset of BFT ? Or they are two different categories?

Please note that there is a similar question here (BFT VS Bitcoin PoW VS PBFT) but without any answer.
Can we say that Proof-of-work is a type of Byzantine fault tolerance
  (BFT) ? In other words, is PoW a subset of BFT?


Yeah I think you can say that.

Proof-of-work is a proposed (and pretty well tested at this point) solution to the Byzantine Generals Problem, and therefore achieves Byzantine Fault Tolerance. The Byzantine faults that it solves includes the classic double spend.

The Byzantine Generals Problem is an illustration of the difficulty in arriving at consensus in a distributed network.