The Craftsman Edger Model 536-871200 uses a Tillotson HU series carburetor. This carburetor is also used on other models of Craftsman edgers, as well as edgers from other manufacturers. The Tillotson HU carburetor is a single-stage carburetor that is designed for use with small engines. It is a relatively simple carburetor to rebuild, and parts are readily available.
Here is a link to a website where you can find more information about the Tillotson HU carburetor:
https://www.tillotson.com/carburetors/hu-series/