Setting reference frame for shapefile with pyshp?

Question

I'm using pyshp to create new shapefiles with Python 3. My code runs without errors, but when I open the resulting file in ArcMap I get this error:

The following datasource you added is missing spatial reference information.

This is not surprising, since I never told my code that the coordinates in the shapefile are supposed to be in EPSG:3006. How do I set this property in pyshp?

Here's some short example code. I want to tell the writer shape that the coordinates in start and stop are in EPSG:3006.

import shapefile

start = [6400137, 321751]  # Coordinates in EPSG:3006
stop  = [6400095, 319357]  # Coordinates in EPSG:3006

with shapefile.Writer("my_shapefile") as shape:
    shape.fileType = 3 # Polyline
    shape.field("FOO", "C", size = 32)
    shape.field("BAR", "C", size = 32)
    shape.line([[start, stop]])
    shape.record("foo", "bar")