Turkish Journal of Mathematics
DOI
10.3906/mat-1206-16
Abstract
In this article, given a category X, with \Omega the subobject classifier in Set^{X^{op}, we set up a one-to-one correspondence between certain (i) classes of X-morphisms, (ii) \Omega-subpresheaves, (iii) \Omega-automorphisms, and (iv) universal operators. As a result we give necessary and sufficient conditions on a morphism class so that the associated (i) \Omega-subpresheaf is a (weak) Grothendieck topology, (ii) \Omega-automorphism is a (weak) Lawvere--Tierney topology, and (iii) universal operation is an (idempotent) universal closure operation. We also finally give several examples of morphism classes yielding (weak) Grothendieck topologies, (weak) Lawvere--Tierney topologies, and (idempotent) universal closure operations.
First Page
818
Last Page
829
Recommended Citation
HOSSEINI, SEYED NASER and NODEHI, MEHDI
(2013)
"Morphism classes producing (weak) Grothendieck topologies, (weak) Lawvere--Tierney topologies, and universal closure operations,"
Turkish Journal of Mathematics: Vol. 37:
No.
5, Article 9.
https://doi.org/10.3906/mat-1206-16
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss5/9
