|
In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree-1 maps between them. It was introduced by . ==Definition== The cyclic category Λ has one object Λ''n'' for each natural number ''n'' = 0, 1, 2, ... The morphisms from Λ''m'' to Λ''n'' are represented by increasing functions ''f'' from the integers to the integers, such that ''f''(''x''+''m''+''1'') = ''f''(''x'')+''n''+''1'', where two functions ''f'' and ''g'' represent the same morphism when their difference is divisible by ''n''+''1''. Informally, the morphisms from Λ''m'' to Λ''n'' can be thought of as maps of (oriented) necklaces with ''m''+1 and ''n''+1 beads. More precisely, the morphisms can be identified with homotopy classes of degree 1 increasing maps from ''S''1 to itself that map the subgroup Z/(''m''+1)Z to Z/(''n''+1)Z. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cyclic category」の詳細全文を読む スポンサード リンク
|