マックレーンの一貫性定理
モノイド圏の一貫性は難しい。定理の記述も色々ある。http://ocw.mit.edu/courses/mathematics/18-769-topics-in-lie-theory-tensor-categories-spring-2009/lecture-notes/MIT18_769S09_lec03.pdf にある次の形が使いやすいように思う。
Let X1, ..., Xn ∈ C. Let P1, P2 be any two parenthesized products of X1, ..., Xn (in this order) with arbitrary insertions of unit objects 1. Let f, g : P1 → P2 be two isomorphisms, obtained by composing associativity and unit isomorphisms and their inverses possibly tensored with identity morphisms.
Then f = g.
一貫性に関しては、
- https://ncatlab.org/nlab/show/coherence+theorem+for+monoidal+categories
- https://ncatlab.org/nlab/show/Mac+Lane%27s+proof+of+the+coherence+theorem+for+monoidal+categories
同値な厳密化定理は、
