Aggregate Function on Uniqueidentifier (GUID)

Just cast it as a BINARY(16).

SELECT category, MIN(CAST(guid AS BINARY(16)))
FROM myTable
GROUP BY category

You can cast it back later if necessary.

WITH CategoryValue
AS
(    
    SELECT category, MIN(CAST(guid AS BINARY(16)))
    FROM myTable
    GROUP BY category
)
SELECT category, CAST(guid AS UNIQUEIDENTIFIER)
FROM CategoryValue