On endomorphism algebras of separable monoidal functors

Brian Day; Craig Pastro

On endomorphism algebras of separable monoidal functors

Brian Day^*, Craig Pastro

^*Corresponding author for this work

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

Abstract

We show that the (co)endomorphism algebra of a sufficiently separable "fibre" functor into Vect_κ, for κ a field of characteristic 0, has the structure of what we call a "unital" von Neumann core in Vect_κ. For Vect_κ, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.

Original language	English
Pages (from-to)	77-96
Number of pages	20
Journal	Theory and Applications of Categories
Volume	22
Publication status	Published - 28 Jan 2009

Keywords

Bialgebra
Separable fibre functor
Tannaka reconstruction
Von Neumann core

Cite this

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title = "On endomorphism algebras of separable monoidal functors",

abstract = "We show that the (co)endomorphism algebra of a sufficiently separable {"}fibre{"} functor into Vectκ, for κ a field of characteristic 0, has the structure of what we call a {"}unital{"} von Neumann core in Vectκ. For Vectκ, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.",

keywords = "Bialgebra, Separable fibre functor, Tannaka reconstruction, Von Neumann core",

author = "Brian Day and Craig Pastro",

year = "2009",

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day = "28",

language = "English",

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journal = "Theory and Applications of Categories",

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publisher = "Mount Allison University",

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T1 - On endomorphism algebras of separable monoidal functors

AU - Day, Brian

AU - Pastro, Craig

PY - 2009/1/28

Y1 - 2009/1/28

N2 - We show that the (co)endomorphism algebra of a sufficiently separable "fibre" functor into Vectκ, for κ a field of characteristic 0, has the structure of what we call a "unital" von Neumann core in Vectκ. For Vectκ, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.

AB - We show that the (co)endomorphism algebra of a sufficiently separable "fibre" functor into Vectκ, for κ a field of characteristic 0, has the structure of what we call a "unital" von Neumann core in Vectκ. For Vectκ, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.

KW - Bialgebra

KW - Separable fibre functor

KW - Tannaka reconstruction

KW - Von Neumann core

UR - https://www.scopus.com/pages/publications/65749119471

M3 - Article

AN - SCOPUS:65749119471

SN - 1201-561X

VL - 22

SP - 77

EP - 96

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

ER -

On endomorphism algebras of separable monoidal functors

Abstract

Keywords

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