Accepted author manuscript
Licence: None
Research output: Contribution to Journal/Magazine › Journal article
Research output: Contribution to Journal/Magazine › Journal article
}
TY - JOUR
T1 - Slices of groupoids are group-like
AU - Cooney, Nicholas
AU - Grabowski, Jan
PY - 2020/2/7
Y1 - 2020/2/7
N2 - Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that every morphism is invertible, then its slices are (connected) groupoids. We give a number of constructions that show how slices of groupoids have properties even closer to those of groups than the groupoids they come from. These include natural notions of kernels and coset spaces.
AB - Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that every morphism is invertible, then its slices are (connected) groupoids. We give a number of constructions that show how slices of groupoids have properties even closer to those of groups than the groupoids they come from. These include natural notions of kernels and coset spaces.
M3 - Journal article
JO - arxiv.org
JF - arxiv.org
ER -