Geodesic
Bicategorical traces and cotraces
Theory and applications of categories, Tome 41 (2024), pp. 707-759

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

The familiar trace of a square matrix generalizes to a trace of an endomorphism of a dualizable object in a symmetric monoidal category. To extend these ideas to other settings, such as modules over non-commutative rings, the trace can be generalized to a bicategory equipped with additional structure called a shadow. We propose a notion of bicategorical cotrace of certain maps involving dualizable objects in a closed bicategory equipped with a coshadow, and we use this framework to draw connections to work of Lipman on residues and traces with Hochschild (co)homology, and to work of Ganter and Kapranov on 2-representations and 2-characters.

Publié le :
Classification : 16D90, 18D15, 18M05, 18M30, 18N10
Keywords: bicategory, cotrace, Hochschild homology, Morita equivalence, shadow, string diagram, trace 
@article{TAC_2024_41_a21,
     author = {Justin Barhite},
     title = {Bicategorical traces and cotraces},
     journal = {Theory and applications of categories},
     pages = {707--759},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a21/}
}
TY  - JOUR
AU  - Justin Barhite
TI  - Bicategorical traces and cotraces
JO  - Theory and applications of categories
PY  - 2024
SP  - 707
EP  - 759
VL  - 41
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2024_41_a21/
LA  - en
ID  - TAC_2024_41_a21
ER  - 
%0 Journal Article
%A Justin Barhite
%T Bicategorical traces and cotraces
%J Theory and applications of categories
%D 2024
%P 707-759
%V 41
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2024_41_a21/
%G en
%F TAC_2024_41_a21
Justin Barhite. Bicategorical traces and cotraces. Theory and applications of categories, Tome 41 (2024), pp. 707-759. http://geodesic.mathdoc.fr/item/TAC_2024_41_a21/