Swallowtail (film) 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 set in Tokyo at an unspecified point in the near
Comma category by Lawvere, which involved the comma punctuation mark. Although standard notation has changed, since the use of a comma as an operator is potentially confusing, and even Lawvere dislikes the uninformative term "comma category" (Lawvere, 1963 p. 13), the name persists. The most general comma category construction involves two functors with the same codomain. Often one of these will have domain 1 (the one-object one-morphism category). Some accounts of category theory consider only these special cases, but the term comma category is actually much more general. Suppose that formula_1, formula_2, and formula_3 are categories, and formula_4 and formula_5 (for source