Geodesic
Monoid-like definitions of cyclic operad
Theory and applications of categories, Tome 32 (2017), pp. 396-436

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

Guided by the microcosm principle of Baez-Dolan and by the algebraic definitions of operads of Kelly and Fiore, we introduce two ``monoid-like'' definitions of cyclic operads, one for the original, ``exchangable-output'' characterisation of Getzler-Kapranov, and the other for the alternative ``entries-only'' characterisation, both within the category of Joyal's species of structures. Relying on a result of Lamarche on descent for species, we use these "monoid-like" definitions to prove the equivalence between the ``exchangable-output'' and ``entries-only'' points of view on cyclic operads.

Publié le :
Classification : 18D50, 18D10, 05A99
Keywords: operads, cyclic operads, species of structures, monoid, microcosm principle 
@article{TAC_2017_32_a11,
     author = {Jovana Obradovic},
     title = {Monoid-like definitions of cyclic operad},
     journal = {Theory and applications of categories},
     pages = {396--436},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a11/}
}
TY  - JOUR
AU  - Jovana Obradovic
TI  - Monoid-like definitions of cyclic operad
JO  - Theory and applications of categories
PY  - 2017
SP  - 396
EP  - 436
VL  - 32
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2017_32_a11/
LA  - en
ID  - TAC_2017_32_a11
ER  - 
%0 Journal Article
%A Jovana Obradovic
%T Monoid-like definitions of cyclic operad
%J Theory and applications of categories
%D 2017
%P 396-436
%V 32
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2017_32_a11/
%G en
%F TAC_2017_32_a11
Jovana Obradovic. Monoid-like definitions of cyclic operad. Theory and applications of categories, Tome 32 (2017), pp. 396-436. http://geodesic.mathdoc.fr/item/TAC_2017_32_a11/