To put it another way, the Seii Taishogun was the one who placed a private position called Kamakura-dono to rule as a leader of the warriors of eastern Japan, Shugo and Jito throughout the country, was recognized as Udaisho with the authority to exercise military police powers, had family organs of clan governance treated the same as official government offices, and bundled it all together and officially secured it.
つまり、東国武士の棟梁として君臨する鎌倉殿という私的地位・守護・地頭を全国に置き、軍事警察権を行使する権限右大将として認知された、家政機関を政所などの公的な政治機関に準ずる扱いを受ける権限を、全て纏め上げて公的に担保するのが征夷大将軍職であった。