自然范畴的一点注记

A note on natural categories

设C,D是两个范畴,S,T∶C→D是两个函子,η∶S→T是自然变换,另外T0T1C→C×2分别是顶函子和底函子,μ∶T0→T1是自然变换.给出由μ和η分别确定的自然范畴Nat(μ)与Nat(η)间的关系,最后用一个例子说明了这个关系.

Let C and D be two categories,and S,T∶C→D two functors,η∶S→T be natural transformation.If T0,T1∶C→C×2 are top functor and bottom functor respectively,and if μ∶T0→T1 is a natural transformation,then we gives the relation between two natural categories Nat（μ） and Nat（η）.Finally,we illustrate this relation by an example.