20/05/29 16:49:30 L93mHa1Z.net
>>135
>[cf. [FrdI], Appendix, Definition A.1, (ii)],
>[FrdI] S. Mochizuki, The Geometry of Frobenioids I: The General Theory, Kyushu J. Math. 62 (2008), pp. 293-400.
下記か
ほんと、これは堪らんな～ｗ（＾＾；
無限後退感ありありですねｗｗ
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THE GEOMETRY OF FROBENIOIDS I:
THE GENERAL THEORY
Shinichi Mochizuki
June 2008
(抜粋)
P118
Appendix: Slim Exponentiation
In the present Appendix, we discuss some elementary general nonsense concerning slim categories.
Definition A.1.
(i) A 2-category of 1-categories will be called 2-slim [cf. [Mzk7], Definition
1.2.4, (iii)] if every 1-morphism [i.e., functor] in the 2-category has no nontrivial
automorphisms.
(ii) If D is a 2-category of 1-categories, then we shall write
|D|
for the associated 1-category whose objects are objects of D and whose morphisms
are isomorphism classes of morphisms of D [cf. [Mzk7], Definition 1.2.4, (iv)]. We
shall also refer to |D| as the coarsification of C.
Remark A.1.1. The name “coarsification” is motivated by the theory of “coarse
moduli spaces” associated to (say) “fine moduli stacks” [cf. [Mzk7], Remark 1.2.4.1].
The following result may be regarded as a generalization of [Mzk7], Proposition
1.2.5, (ii) [a result concerning anabelioids], to the case of arbitrary slim categories.