Swallowtail butterfly passed in a pupal diapause stage. As swallowtail butterflies are large, colorful, and attractive, they were once targeted by butterfly collectors. The largest of these, the birdwing butterflies are particularly sought after and are cultured in butterfly farms for the purpose of collectors. Many members of the family feed as larvae on plants of the citrus family, Rutaceae. Some of these attractive butterflies are therefore considered pests in citrus orchards. The Oregon swallowtail is the state insect of Oregon. The eastern tiger swallowtail is the state insect of Virginia and the state butterfly of Georgia, Delaware, and South Carolina. The
Comma category exists. Lawvere showed that the functors formula_169 and formula_170 are adjoint if and only if the comma categories formula_171 and formula_172, with formula_173 and formula_174 the identity functors on formula_175 and formula_3 respectively, are isomorphic, and equivalent elements in the comma category can be projected onto the same element of formula_177. This allows adjunctions to be described without involving sets, and was in fact the original motivation for introducing comma categories. If the domains of formula_178 are equal, then the diagram which defines morphisms in formula_179 with formula_180 is identical to the diagram which defines a natural transformation formula_181. The