Variation on a comprehensive theme: dedicated to the memory of RFC (Bob) Walters

Ross Street

Variation on a comprehensive theme: dedicated to the memory of RFC (Bob) Walters

^*Corresponding author for this work

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Abstract

The main result concerns a bicategorical factorization system on the bi-category Cat of categories and functors. Each functor A ->(f) B factors up to isomorphism as A ->(j) E ->(p) B where j is what we call an ultimate functor and p is what we call a groupoid fibration. Every right adjoint functor is ultimate. Functors whose ultimate factor is a right adjoint are shown to have bearing on the theory of polynomial functors.

Original language	English
Pages (from-to)	964-978
Number of pages	16
Journal	Theory and Applications of Categories
Volume	37
Publication status	Published - 2021

Keywords

factorization system
bicategory
fibration
final functor

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http://www.tac.mta.ca/tac/volumes/37/29/37-29abs.htmlLicence: Unspecified

Cite this

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title = "Variation on a comprehensive theme: dedicated to the memory of RFC (Bob) Walters",

abstract = "The main result concerns a bicategorical factorization system on the bi-category Cat of categories and functors. Each functor A ->(f) B factors up to isomorphism as A ->(j) E ->(p) B where j is what we call an ultimate functor and p is what we call a groupoid fibration. Every right adjoint functor is ultimate. Functors whose ultimate factor is a right adjoint are shown to have bearing on the theory of polynomial functors.",

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year = "2021",

language = "English",

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journal = "Theory and Applications of Categories",

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AB - The main result concerns a bicategorical factorization system on the bi-category Cat of categories and functors. Each functor A ->(f) B factors up to isomorphism as A ->(j) E ->(p) B where j is what we call an ultimate functor and p is what we call a groupoid fibration. Every right adjoint functor is ultimate. Functors whose ultimate factor is a right adjoint are shown to have bearing on the theory of polynomial functors.

KW - factorization system

KW - bicategory

KW - fibration

KW - final functor

UR - http://purl.org/au-research/grants/arc/DP190102432

M3 - Article

SN - 1201-561X

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EP - 978

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

ER -

Variation on a comprehensive theme: dedicated to the memory of RFC (Bob) Walters

Abstract

Keywords

Access to Document

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Working synthetically in higher categorical structures

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Variation on a comprehensive theme: dedicated to the memory of RFC (Bob) Walters

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Working synthetically in higher categorical structures

Cite this