Polygonia comma and by the row of pale submarginal spots on the hindwing upperside, which tend to be separate and surrounded by dark shading in comma, but are larger and tend to run together into a pale band in "P. satyrus". Polygonia comma Polygonia comma, the eastern comma, is a North American butterfly in the family Nymphalidae, subfamily Nymphalinae. This butterfly is seasonally variable. The upperside of the summer form's hindwings are all black, whereas the winter forms hindwings are reddish orange. The underside of both forms is striped with dark and light brown. There is a silvery comma mark in the
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