Two-dimensional monadicity

John Bourke

doi:10.1016/j.aim.2013.11.007

Two-dimensional monadicity

John Bourke^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in that, to fully express the behaviour that occurs, one needs to be able to quantify over strict morphisms amongst the weaker kinds. F-categories were introduced to express this interplay between strict and weak morphisms. We express doctrinal adjunction as an F-categorical lifting property and use this to give monadicity theorems, expressed using the language of F-categories, that cover each weaker kind of morphism.

Original language	English
Pages (from-to)	708-747
Number of pages	40
Journal	Advances in Mathematics
Volume	252
DOIs	https://doi.org/10.1016/j.aim.2013.11.007
Publication status	Published - 15 Feb 2014
Externally published	Yes

Keywords

2-category
2-monad
F-category
Monadicity
Primary
Weak morphism

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10.1016/j.aim.2013.11.007

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AB - The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in that, to fully express the behaviour that occurs, one needs to be able to quantify over strict morphisms amongst the weaker kinds. F-categories were introduced to express this interplay between strict and weak morphisms. We express doctrinal adjunction as an F-categorical lifting property and use this to give monadicity theorems, expressed using the language of F-categories, that cover each weaker kind of morphism.

KW - 2-category

KW - 2-monad

KW - F-category

KW - Monadicity

KW - Primary

KW - Weak morphism

UR - https://www.scopus.com/pages/publications/84890399809

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SN - 0001-8708

VL - 252

SP - 708

EP - 747

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Two-dimensional monadicity

Abstract

Keywords

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