Scarce swallowtail Scarce swallowtail The scarce swallowtail ("Iphiclides podalirius") is a butterfly belonging to the family Papilionidae. It is also called the sail swallowtail or pear-tree swallowtail. Subspecies include: "Iphiclides podalirius feisthamelii" is sometimes treated as a valid species, "Iphiclides feisthamelii". Despite the name "scarce swallowtail", this species is quite common. The scarcity of United Kingdom migrants is responsible for the English vernacular name. This species is widespread in the East Palearctic ecozone and in most of Europe with the exception of the northern parts. Its range extends northwards to Lower Lusatia and central Poland and eastwards across Asia Minor and Transcaucasia
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