Geodesic
Pseudocommutativity and lax idempotency for relative pseudomonads
Theory and applications of categories, Tome 39 (2023), pp. 1018-1049.

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

We extend the classical work of Kock on strong and commutative monads, as well as the work of Hyland and Power for 2-monads, in order to define strong and pseudocommutative relative pseudomonads. To achieve this, we work in the more general setting of 2-multicategories rather than monoidal 2-categories. We prove analogous implications to the classical work: that a strong relative pseudomonad is a pseudo-multifunctor, and that a pseudocommutative relative pseudomonad is a multicategorical pseudomonad. Furthermore, we extend the work of López Franco with a proof that a lax-idempotent strong relative pseudomonad is pseudocommutative. We apply the results of this paper to the example of the presheaf relative pseudomonad.
Publié le :
Classification : Primary 18N15, Secondary 18D65, 18A05, 18M65
Keywords: category theory, monad theory, presheaf 
@article{TAC_2023_39_a33,
     author = {Andrew Slattery},
     title = {Pseudocommutativity and lax idempotency for relative pseudomonads},
     journal = {Theory and applications of categories},
     pages = {1018--1049},
     publisher = {mathdoc},
     volume = {39},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a33/}
}
TY  - JOUR
AU  - Andrew Slattery
TI  - Pseudocommutativity and lax idempotency for relative pseudomonads
JO  - Theory and applications of categories
PY  - 2023
SP  - 1018
EP  - 1049
VL  - 39
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2023_39_a33/
LA  - en
ID  - TAC_2023_39_a33
ER  - 
%0 Journal Article
%A Andrew Slattery
%T Pseudocommutativity and lax idempotency for relative pseudomonads
%J Theory and applications of categories
%D 2023
%P 1018-1049
%V 39
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2023_39_a33/
%G en
%F TAC_2023_39_a33
Andrew Slattery. Pseudocommutativity and lax idempotency for relative pseudomonads. Theory and applications of categories, Tome 39 (2023), pp. 1018-1049. http://geodesic.mathdoc.fr/item/TAC_2023_39_a33/