How to have a keymap work in object mode and edit mode?

Question

I've created an operator that uses a keymap to activate it. While it works in object mode, it is not being called in edit mode. Is there a way to get this to run in edit mode too?

import bpy
class GridRescale(bpy.types.Operator):
    """Change grid scale"""
    bl_idname = "kitfox.grid_rescale"
    bl_label = "Grid Rescale"
    bl_options = {'REGISTER'}
def invoke(self, context, event):
    scale = bpy.context.space_data.overlay.grid_scale

    if event.type == "LEFT_ARROW":
        scale /= 2
    elif  event.type == "RIGHT_ARROW":
        scale *= 2

    bpy.context.space_data.overlay.grid_scale = scale
    self.report({'INFO'}, "Grid scale: %f" % (scale))
    return {'FINISHED'}



store keymaps here to access after registration
addon_keymaps = []
def register():
    bpy.utils.register_class(GridRescale)
# handle the keymap
wm = bpy.context.window_manager
km = wm.keyconfigs.addon.keymaps.new(name='Object Mode', space_type='EMPTY')

kmi = km.keymap_items.new(GridRescale.bl_idname, 'LEFT_ARROW', 'PRESS', ctrl=True, shift=False)
kmi = km.keymap_items.new(GridRescale.bl_idname, 'RIGHT_ARROW', 'PRESS', ctrl=True, shift=False)

addon_keymaps.append(km)




def unregister():
    bpy.utils.unregister_class(GridRescale)
# handle the keymap
wm = bpy.context.window_manager
for km in addon_keymaps:
    wm.keyconfigs.addon.keymaps.remove(km)
# clear the list
del addon_keymaps[:]



if name == "main":
    register()