Geodesic
Span, cospan, and other double categories
Theory and applications of categories, Tome 26 (2012), pp. 729-742 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

Voir la notice de l'article

Given a double category $\mathbb D$ such that $\mathbb D_0$ has pushouts, we characterize oplax/lax adjunctions between $\mathbb D$ and $Cospan(\mathbb D_0)$ for which the right adjoint is normal and restricts to the identity on $\mathbb D_0$, where $Cospan(\mathbb D_0)$ is the double category on $\mathbb D_0$ whose vertical morphisms are cospans. We show that such a pair exists if and only if $\mathbb D$ has companions, conjoints, and 1-cotabulators. The right adjoints are induced by the companions and conjoints, and the left adjoints by the 1-cotabulators. The notion of a 1-cotabulator is a common generalization of the symmetric algebra of a module and Artin-Wraith glueing of toposes, locales, and topological spaces.

Publié le :
Classification : 18D05, 18A40, 18B25, 18B30, 06D22, 18D10, 15A78
Keywords: double category, lax functor, (co)span, (co)tabulator, companion, conjoint, symmetric algebra 
@article{TAC_2012_26_a25,
     author = {Susan Niefield},
     title = {Span, cospan, and other double categories},
     journal = {Theory and applications of categories},
     pages = {729--742},
     year = {2012},
     volume = {26},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_26_a25/}
}
TY  - JOUR
AU  - Susan Niefield
TI  - Span, cospan, and other double categories
JO  - Theory and applications of categories
PY  - 2012
SP  - 729
EP  - 742
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/TAC_2012_26_a25/
LA  - en
ID  - TAC_2012_26_a25
ER  - 
%0 Journal Article
%A Susan Niefield
%T Span, cospan, and other double categories
%J Theory and applications of categories
%D 2012
%P 729-742
%V 26
%U http://geodesic.mathdoc.fr/item/TAC_2012_26_a25/
%G en
%F TAC_2012_26_a25
Susan Niefield. Span, cospan, and other double categories. Theory and applications of categories, Tome 26 (2012), pp. 729-742. http://geodesic.mathdoc.fr/item/TAC_2012_26_a25/