## From Coherent Structures to Universal Properties (1999)

Venue: | J. Pure Appl. Algebra |

Citations: | 12 - 2 self |

### BibTeX

@ARTICLE{Hermida99fromcoherent,

author = {Claudio Hermida},

title = {From Coherent Structures to Universal Properties},

journal = {J. Pure Appl. Algebra},

year = {1999},

volume = {165},

pages = {7--61}

}

### OpenURL

### 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: • S has the adjoint-pseudo-algebra property. • 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 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 monoid classifiers) as well as pseudo-functors into Cat.

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