Compact closed bicategories (Q2826239)

A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual. This means that the zig-zag identities of duality only hold up-to isomorphisms which are subject themselves to coherence conditions (the so-called `swallowtail identities').NEWLINENEWLINEGiven a 2-category with finite products and weak pullbacks, the bicategory of its objects, spans, and isomorphism classes of maps of spans is proven to be a compact closed bicategory. Examples include the bicategory of spans of sets; and certain bicategories of `resistor networks'.NEWLINENEWLINEThe paper contains nice and detailed definitions of the occurring structures; such as a bicategory, a monoidal bicategory, a braided monoidal bicategory, a sylleptic monoidal bicategory, a symmetric monoidal bicategory, a symmetric monoidal closed bicategory, and a compact closed bicategory.