Red-bodied swallowtail Red-bodied swallowtail Red-bodied swallowtails are butterflies in the swallowtail family, that belong to the genera "Atrophaneura", "Byasa", "Losaria", or "Pachliopta". They are generally found in Asia (Indomalaya ecozone). Collectors have found the red-bodied swallowtails difficult to kill. Pinching the thorax, a method which kills most butterflies, is withstood and apparently only stuns the butterfly temporarily. The eggs are simple. The larvae resemble those of other Troidini. Fleshy spine-like tubercles, often with red tips, line the caterpillars' backs, and their bodies are dark red to brown and velvety black or shades of grey with a pattern of black lines. They feed
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