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There are many different types of lenses, but largely they fall into the three classes of the title: set-based, delta-based and edit-based lenses. This paper develops some of the general relationships between those classes. The main results are that a category of set-based lenses is a full subcategory of a category of delta-based lenses determined by sending sets to codiscrete categories; that symmetric set-based lenses can similarly be seen as symmetric delta-based lenses; that symmetricdblp:conf/etaps/JohnsonR16 fatcat:5rg3fj45zzd5plqzy2h4uurwna