Scarce swallowtail Republic have been found to be a good indicator of relatively well preserved xerothermic grassland habitats with forest-steppe vegetation, which have no cutting history. In some years the scarce swallowtail is quite abundant. The scarce swallowtail is getting rarer as the blackthorn bushes are being cleared. The butterfly is now protected by law in the Czech Republic, Slovakia, Germany, Hungary, Luxembourg, Russia, Ukraine and Poland. It is considered rare and endangered and protected in some provinces of Austria and of indeterminate status throughout Europe. In Armenia the species demonstrates stable population trend and is evaluated as Least Concern. Though referred
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