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MB3 126a: Trapping Sleeping, Blind, Lame or Old Animals on Shabbos (316:2-3)
Trapping an animal that is sleeping/blind is still prohibited on Shabbos since they generally run away if they sense a person nearby. If it can't get away (e.g. lame), the prohibition is only d'rabbanan. Causing a dog to trap an animal for you on Shabbos. Arresting a person on Shabbos vis-a-vis trapping. Trapping a fly is צידה מדרבנן.