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*To*: categories@mta.ca*Subject*: categories: coherence => universality (preprint)*From*: Claudio Hermida <hermida@maths.usyd.edu.au>*Date*: Mon, 15 Nov 1999 08:49:41 +1100*Organization*: School of Mathematics and Statistics, University of Sydney*Sender*: cat-dist@mta.ca

The preprint "From coherent structures to universal properties" is available from http://www.maths.usyd.edu.au:8000/u/hermida under coh-univ.ps Abstract: Given a 2-category K admitting a calculus of bimodules, and a 2-monad T on it compatible with such calculus, we construct a 2-category L with a 2-monad S on it such that: i) S has the adjoint-pseudo-algebra property. ii) The 2-categories of pseudo-algebras of S and T are equivalent. Thus, coherent structures (pseudo-T-algebras) are transformed into universally characterised ones (adjoint-pseudo-S-algebras). The 2-category L consists of lax algebras for the pseudo-monad induced by T on the bicategory of bimodules of K. We give an intrinsic characterisation of pseudo-S-algebras in terms of {\em representability\/}. Two major consequences of the above transformation are the classifications of lax and strong morphisms, with the attendant coherence result for pseudo-algebras. We apply the theory in the context of internal categories and examine monoidal and monoidal globular categories (including their {\em monoid classifiers\/}) as well as pseudo-functors into Cat. -- Claudio Hermida School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW 2006, Australia

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