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Openness with Respect to a Closure Operator |
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| Authors: | Eraldo Giuli Walter Tholen |
| Affiliation: | (1) Dipartimento di Matematica Pura ed Applicata, Università degli Studi di L'Aquila, via Vetoio, loc. Coppito –, 67100 L'Aquila, Italy, e-mail;(2) Department of Mathematics and Statistics, York University, North York, Ontario, Canada, M3J 1P3 e-mail |
| Abstract: | We study the notions of closed, open, initial and final morphism with respect to a closure operator and show that they have a perfectly symmetric pullback behaviour. We also investigate their interaction with closed and with open subobjects and the impact of the existence of suitably defined complements of subobjects. |
| Keywords: | closure operator closed morphism open morphism initial morphism final morphism open subobject natural complement |
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