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On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions

Hans-Jürgen Vogel (2001)

Discussiones Mathematicae - General Algebra and Applications

The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family d = ( d A : A A A | A | R e l | ) of diagonal morphisms, a family t = ( t A : A I | A | R e l | ) of terminal morphisms, and a family = ( A : A A A | A | R e l | ) of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....

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