Strictification

<h2 id="monoidal-category">Monoidal category</h2>
<ul><li>Every <a href="/facts/Monoidal_category/F2l5oKMD">monoidal category</a> is monoidally equivalent to a strict monoidal category.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> This is (essentially) the <a href="/facts/Mac_Lane_coherence_theorem/xd5737PG">Mac Lane coherence theorem</a>.</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Coherence_condition/KPbATej5">Coherence condition</a></li></ul>
<h2 id="notes">Notes</h2>

<h2 id="reference">Reference</h2>
<ul><li>Schauenburg, Peter (2001). <a href="http://eudml.org/doc/121925">"Turning monoidal categories into strict ones"</a>. <i>The New York Journal of Mathematics [Electronic Only]</i>. 7: 257–265. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/1076-9803">1076-9803</a>.</li>
<li><a href="/facts/Andr%25C3%25A9_Joyal/Xc0dKuXB">Joyal, A.</a>; <a href="/facts/Ross_Street/1wXoGIte">Street, R.</a> (1993). <a href="https://doi.org/10.1006%2Faima.1993.1055">"Braided Tensor Categories"</a>. <i><a href="/facts/Advances_in_Mathematics/kXtcl4pM">Advances in Mathematics</a></i>. 102 (1): 20–78. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1006%2Faima.1993.1055">10.1006/aima.1993.1055</a>.</li>
<li>Lack, Stephen (2002). "Codescent objects and coherence". <i>Journal of Pure and Applied Algebra</i>. 175 (1–3): 223–241. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2FS0022-4049%2802%2900136-6">10.1016/S0022-4049(02)00136-6</a>.</li>
<li>Mac Lane, Saunders (1978). "Symmetry and Braidings in Monoidal Categories". <a href="https://books.google.com/books?id=MXboNPdTv7QC&pg=PA257"><i>Categories for the Working Mathematician</i></a>. Graduate Texts in Mathematics. Vol. 5. pp. 251–266. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4757-4721-8_12">10.1007/978-1-4757-4721-8_12</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4419-3123-8. §3. Strict Monoidal Categories</li>
<li>Shulman, Michael A. (2012). "Not every pseudoalgebra is equivalent to a strict one". <i>Advances in Mathematics</i>. 229 (3): 2024–2041. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/1005.1520">1005.1520</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.aim.2011.01.010">10.1016/j.aim.2011.01.010</a>.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li>Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor. <a href="https://ocw.mit.edu/courses/18-769-topics-in-lie-theory-tensor-categories-spring-2009/resources/mit18_769s09_lec02/">"18.769, Spring 2009, Graduate Topics in Lie Theory: Tensor Categories §.Lecture 2"</a>. <i>MIT Open Course Ware</i>.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Schauenburg 2001 - Schauenburg, Peter (2001). "Turning monoidal categories into strict ones". The New York Journal of Mathematics [Electronic Only]. 7: 257–265. ISSN 1076-9803. <a href="http://eudml.org/doc/121925" target="_blank">http://eudml.org/doc/121925</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Strictification open-in-new

Strictification