Holgate, DavidSlapal, Josef2019-10-222019-10-222018Holgate, D , Slapal, J . (2018). Closure, interior and neighbourhood in a category. Hacettepe Journal of Mathematics and Statistics , 47 (6) , 1512-1520 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/41011/4948282651-477Xhttp://hdl.handle.net/10566/5059The natural correspondences in topology between closure, interior and neighbourhood no longer hold in an abstract categorical setting where subobject lattices are not necessarily Boolean algebras. We analyse three canonical correspondences between closure, interior and neighbourhood operators in a category endowed with a subobject structure. While these correspondences coincide in general topology, the analysis highlights subtle di erences which distinguish di erent approaches taken in the literature.enCategorical closure operatorInterior operatorNeighbourhood operatorArticle