Swallowtail (film) also nominated for but did not win the following awards: Swallowtail (film) Swallowtail, also known as Swallowtail Butterfly (スワロウテイル "Suwarōteiru"), is a 1996 Japanese crime film directed by Shunji Iwai, starring Hiroshi Mikami, pop-singer Chara, and Ayumi Ito. The film was shot on hand-held cameras using jump cuts and other visual techniques. It covers a wide array of themes and genres, from social realism to coming-of-age to crime. A theme song for the film under "Yen Town Band", titled "Swallowtail Butterfly (Ai no Uta)", gained first place on the Oricon Weekly Singles Chart of October 7, 1996. The film is
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