From Coherent Structures to Universal Properties
| dc.creator | Hermida, Claudio | |
| dc.date | 2000-06-21 | |
| dc.date.accessioned | 2026-07-07T04:36:00Z | |
| dc.date.available | 2026-07-07T04:36:00Z | |
| dc.description | Given a 2-category $\twocat{K}$ admitting a calculus of bimodules, and a 2-monad T on it compatible with such calculus, we construct a 2-category $\twocat{L}$ with a 2-monad S on it such that: (1)S has the adjoint-pseudo-algebra property. (2)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 $\twocat{L}$ consists of lax algebras for the pseudo-monad induced by T on the bicategory of bimodules of $\twocat{K}$. 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 $\Cat$. | |
| dc.description | to appear in Journal of Pure and Applied Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0006161 | |
| dc.identifier | http://arxiv.org/abs/math/0006161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59450 | |
| dc.subject | Category Theory | |
| dc.subject | 18D05,18D10,18D30,18D35,18D50,18C15,18C20 | |
| dc.title | From Coherent Structures to Universal Properties | |
| dc.type | text |