sink drain with washer drain ?

I'm remodeling my kitchen. In the basement the washer drains into a vertical 2 1/2" pipe that stands about 4 feet tall. Is there a problem with running the new kitchen sink drain into that also? I can put a Y on top. Thanks!

You can't dump an upstairs fixture into the top of the downstairs fixture.
It siphons the p-trap.

Any would would need to come in below the tee and p-trap.
The vent for the downstairs fixture would need to tie into the vent above at 42" above the floor.