4K video editing does not actually require a 4K monitor. Most editing applications will automatically reduce your video resolution without you ever knowing.
However, just because you can't doesn't mean you should.
If you are delivering 4K footage to your clients or the ultimate file destination it is highly recommended to view that footage in 4K.
The extra pixels in 4K could influence the look of your footage in a less-than-desirable way.
However, if you're shooting in 4K and delivering in HD, which is very common it really doesn't matter if you don't have a 4K monitor.