Skip to main content

Research Repository

Advanced Search

Quantum field theories on categories fibered in groupoids

Benini, Marco; Schenkel, Alexander


Marco Benini


We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first examples of homotopical quantum field theories resembling some aspects of gauge theories.


Benini, M., & Schenkel, A. (2017). Quantum field theories on categories fibered in groupoids. Communications in Mathematical Physics, 356(1), 19-64.

Journal Article Type Article
Acceptance Date Jul 7, 2017
Online Publication Date Aug 24, 2017
Publication Date 2017-11
Deposit Date Aug 21, 2017
Publicly Available Date Aug 24, 2017
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 356
Issue 1
Pages 19-64
Keywords locally covariant quantum field theory, fibered categories, Kan extension, homo-topical algebra, homotopical quantum field theory
Public URL
Publisher URL
Related Public URLs


10.1007_s00220-017-2986-7.pdf (890 Kb)

Copyright Statement
Copyright information regarding this work can be found at the following address:

You might also like

Downloadable Citations