strictification

• Every monoidal category is monoidally equivalent to a strict monoidal category.{{harvnb|Schauenburg|2001}} This is (essentially) the Mac Lane coherence theorem.

• Coherence condition

{{reflist}}

• {{cite journal |url=http://eudml.org/doc/121925 |title=Turning monoidal categories into strict ones |journal=The New York Journal of Mathematics [Electronic Only] |date=2001 |volume=7 |pages=257–265 |last1=Schauenburg |first1=Peter|issn=1076-9803}}
• {{cite journal |doi=10.1006/aima.1993.1055 |doi-access=free |title=Braided Tensor Categories |date=1993 |last1=Joyal |first1=A. |authorlink1=André Joyal |last2=Street |first2=R. |authorlink2=Ross Street |journal=Advances in Mathematics |volume=102 |issue=1 |pages=20–78 }}
• {{cite journal |doi=10.1016/S0022-4049(02)00136-6 |title=Codescent objects and coherence |date=2002 |last1=Lack |first1=Stephen |journal=Journal of Pure and Applied Algebra |volume=175 |issue=1–3 |pages=223–241 }}
• {{cite book |doi=10.1007/978-1-4757-4721-8_12 |chapter=Symmetry and Braidings in Monoidal Categories |title=Categories for the Working Mathematician |series=Graduate Texts in Mathematics |date=1978 |last1=Mac Lane |first1=Saunders |volume=5 |pages=251–266 |isbn=978-1-4419-3123-8|url={{Google books|MXboNPdTv7QC|page=257|plainurl=yes}}}} §3. Strict Monoidal Categories
• {{cite journal |doi=10.1016/j.aim.2011.01.010 |title=Not every pseudoalgebra is equivalent to a strict one |date=2012 |last1=Shulman |first1=Michael A. |journal=Advances in Mathematics |volume=229 |issue=3 |pages=2024–2041 |arxiv=1005.1520 }}

• {{cite web |last1=Etingof |first1=Pavel |last2=Gelaki |first2=Shlomo |last3=Nikshych |first3=Dmitri |last4=Ostrik |first4=Victor |title=18.769, Spring 2009, Graduate Topics in Lie Theory: Tensor Categories §.Lecture 2 |url=https://ocw.mit.edu/courses/18-769-topics-in-lie-theory-tensor-categories-spring-2009/resources/mit18_769s09_lec02/ |website=MIT Open Course Ware}}

Category:Category theory