Lax Extensions of Conical <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="sans-serif">I</mi></mrow></semantics></math></inline-formula>-Semifilter Monads

Abstract

For a quantale I, the unit interval endowed with a continuous triangular norm, we introduce the canonical, op-canonical and Kleisli extensions of the conical I-semifilter monad to I-Rel. It is proved that the op-canonical extension coincides with the Kleisli extension.

Keywords

• lax extension
• conical |-semifilter monad
• Kleisli extension