McKinsey-Tarski Algebras and Raney Extensions

Abstract We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing the construction of the Funayama envelope of a frame. The resulting notion of the $$T_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -hull of a Raney extension generalizes that of the $$T_D$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:math> -hull of a frame.