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memo a

Costa, Laura; Miró-Roig, Rosa María; Pons-Llopis, Joan (2021). Ulrich Bundles. doi:10.1515/9783110647686. ISBN 9783110647686.

memo b

memo c

memo d

Laplaza, Miguel L. (1972). “Coherence for categories with associativity, commutativity and distributivity”. Bulletin of the American Mathematical Society. 78 (2): 220–222. doi:10.1090/S0002-9904-1972-12925-2.

memo g

memo j

\mathrm {Nat} ({\mathcal {A}}(A,-),F)\cong F(A).

memo k

Batanin, M.A. (1998a). “Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories”. Advances in Mathematics. 136: 39–103. doi:10.1006/aima.1998.1724.

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Cheng, Eugenia (2004). “Weak n-categories: Comparing opetopic foundations”. Journal of Pure and Applied Algebra. 186 (3): 219–231. doi:10.1016/S0022-4049(03)00140-3.

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$A\mathrel {\stackrel {\cong }{\longrightarrow }} B$

$A\mathrel {\overset {\cong }{\longrightarrow }} B$

$A{\stackrel {\cong }{\longrightarrow }}B$

$A{\overset {\cong }{\longrightarrow }}B$

$A\mathrel {\mathop {\longrightarrow } ^{\cong }} B$

$A\mathop {\longrightarrow } ^{\cong }B$

memo l

Cicogna, G. (1980). “A method from categories for introducing a general notion of convergence and limit”. Journal of Mathematical Analysis and Applications. 76 (2): 476–482. doi:10.1016/0022-247X(80)90043-8.

Kamps, K. H.; Porter, T. (1997). Abstract Homotopy and Simple Homotopy Theory. doi:10.1142/2215. ISBN 978-981-02-1602-3.

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memo m

^[7]

Wikipedia:Articles for deletion/Associativity isomorphism

Would you tell me more about no consensus? There seems to be consensus that as a standalone article, it does not meet the WP:N. Maybe I should have linked to WP:CFORK in the AfD. Should we discuss merging somewhere other than the AfD? (I thought the consensus was merge.)

Coherence

Kelly, G.M (1964). “On MacLane’s conditions for coherence of natural associativities, commutativities, etc”. Journal of Algebra. 1 (4): 397–402. doi:10.1016/0021-8693(64)90018-3.

Crane, Louis; Yetter, David N. (1998). “Examples of categorification”. Cahiers de Topologie et Géométrie Différentielle Catégoriques. 39 (1): 3–25.

Laplaza, Miguel L. (1972). “Coherence for associativity not an isomorphism”. Journal of Pure and Applied Algebra. 2 (2): 107–120. doi:10.1016/0022-4049(72)90016-3.

Slodičák, Viliam (March 2012). “Toposes are symmetric monoidal closed categories”. Scientific Research of the Institute of Mathematics and Computer Science. 11 (1): 107–116. doi:10.17512/jamcm.2012.1.11.

Kapranov, Mikhail M. (1993). “The permutoassociahedron, Mac Lane’s coherence theorem and asymptotic zones for the KZ equation”. Journal of Pure and Applied Algebra. 85 (2): 119–142. doi:10.1016/0022-4049(93)90049-Y.

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Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor (22 July 2015). “Chapter 2. Monoidal categories”. Tensor Categories. Vol. 205. Providence, Rhode Island: American Mathematical Society. ISBN 9781470434410.

^[10]

Descent

Beck’s monadicity theorem for ∞-category

a fully faithful and essentially surjective functor is an equivalence for quasicategories,

a fully faithful and essentially surjective functor is an equivalence for precategories

Ahrens, Benedikt; Paige Randall North; Shulman, Michael; Tsementzis, Dimitris (2021). “The Univalence Principle (3.2. Categories in HoTT)”. arXiv:2102.06275 [math.CT].

Homotopy coherence

that quasicategories give a model for ∞-categories where diagrams are automatically homotopy coherent.

∞-anafunctor

semi-monoidal category

semi category, Semigroupoid

Exel, R. (May 2011). “Semigroupoid C^⁎ -algebras”. Journal of Mathematical Analysis and Applications. 377 (1): 303–318. doi:10.1016/j.jmaa.2010.10.061.

homotopy inverse

Let $\sim$ be the relation of being homotopic, and $f:X\rightarrow Y$ , $g:Y\rightarrow X$ be two morphisms such that $g\circ f\sim \mathrm {id} _{X}$ . In this case we say that $g$ is a left homotopy inverse to $f$ , and that $f$ is a right homotopy inverse to $g$ .

^ Barr, Michael; Kennison, John F.; Raphael, R. (2009). “Isbell duality for modules”. Theory and Applications of Categories. 22: 401–419. doi:10.70930/tac/1zcfxg2x.
^ Cisinski, Denis-Charles (2007). “Batanin higher groupoids and homotopy types”. Categories in Algebra, Geometry and Mathematical Physics. Contemporary Mathematics. Vol. 431. pp. 171–186. arXiv:math/0604442. doi:10.1090/conm/431/08272. ISBN 978-0-8218-3970-6.
^ Leinster, Tom (2000). “Operads in Higher-Dimensional Category Theory”. arXiv:math/0011106. Bibcode:2000math…..11106L.
^ Boyarchenko, Mitya; Drinfeld, Vladimir (2014). “Character sheaves on unipotent groups in positive characteristic: Foundations”. Selecta Mathematica. 20: 125–235. arXiv:0810.0794. doi:10.1007/s00029-013-0133-7.
^ . doi:10.1090/S0002-9939-1966-0186535-8. ;
^ Isbell, J. R.; Wright, F. B. (1 January 1966). “Another equivalent form of the axiom of choice”. Proceedings of the American Mathematical Society. 17 (1): 174. doi:10.1090/S0002-9939-1966-0186535-8.
^ Handbook of Algebraic Topology (PDF). 1995. doi:10.1016/B978-0-444-81779-2.X5000-7. ISBN 978-0-444-81779-2.
^ Johnson, Niles; Yau, Donald (2020). 2-Dimensional Categories. arXiv:2002.06055. ISBN 9780198871378.
^ Kassel, Christian (1995). “Tensor Categories”. Quantum Groups. Graduate Texts in Mathematics. Vol. 155. pp. 275–293. doi:10.1007/978-1-4612-0783-2_11. ISBN 978-1-4612-6900-7.
^ Lambe, Larry A.; Radford, David E. (1997). “Categorical Constructions and Generalizations of the Quantum Yang-Baxter Equation”. Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach. pp. 249–260. doi:10.1007/978-1-4615-4109-7_9. ISBN 978-1-4613-6842-7.
^ “homotopy inverse”. ncatlab.org.
^ Riehl, Emily (2022). “Homotopical categories: From model categories to (∞, 1)-categories”. Stable Categories and Structured Ring Spectra. pp. 5–74. arXiv:1904.00886. doi:10.1017/9781009128957.002. ISBN 978-1-009-12895-7.
^ Cutler, Tyrone. “Elementary Homotopy Theory I” (PDF).

[1] Barr, Michael; Kennison, John F.; Raphael, R. (2009). “Isbell duality for modules”. Theory and Applications of Categories. 22: 401–419. doi:10.70930/tac/1zcfxg2x.

[2] Cisinski, Denis-Charles (2007). “Batanin higher groupoids and homotopy types”. Categories in Algebra, Geometry and Mathematical Physics. Contemporary Mathematics. Vol. 431. pp. 171–186. arXiv:math/0604442. doi:10.1090/conm/431/08272. ISBN 978-0-8218-3970-6.

[3] Leinster, Tom (2000). “Operads in Higher-Dimensional Category Theory”. arXiv:math/0011106. Bibcode:2000math…..11106L.

[4] Boyarchenko, Mitya; Drinfeld, Vladimir (2014). “Character sheaves on unipotent groups in positive characteristic: Foundations”. Selecta Mathematica. 20: 125–235. arXiv:0810.0794. doi:10.1007/s00029-013-0133-7.

[5] . doi:10.1090/S0002-9939-1966-0186535-8. ;

[6] Isbell, J. R.; Wright, F. B. (1 January 1966). “Another equivalent form of the axiom of choice”. Proceedings of the American Mathematical Society. 17 (1): 174. doi:10.1090/S0002-9939-1966-0186535-8.

[7] Handbook of Algebraic Topology (PDF). 1995. doi:10.1016/B978-0-444-81779-2.X5000-7. ISBN 978-0-444-81779-2.

[8] Johnson, Niles; Yau, Donald (2020). 2-Dimensional Categories. arXiv:2002.06055. ISBN 9780198871378.

[9] Kassel, Christian (1995). “Tensor Categories”. Quantum Groups. Graduate Texts in Mathematics. Vol. 155. pp. 275–293. doi:10.1007/978-1-4612-0783-2_11. ISBN 978-1-4612-6900-7.

[10] Lambe, Larry A.; Radford, David E. (1997). “Categorical Constructions and Generalizations of the Quantum Yang-Baxter Equation”. Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach. pp. 249–260. doi:10.1007/978-1-4615-4109-7_9. ISBN 978-1-4613-6842-7.

[11] “homotopy inverse”. ncatlab.org.

[12] Riehl, Emily (2022). “Homotopical categories: From model categories to (∞, 1)-categories”. Stable Categories and Structured Ring Spectra. pp. 5–74. arXiv:1904.00886. doi:10.1017/9781009128957.002. ISBN 978-1-009-12895-7.

[13] Cutler, Tyrone. “Elementary Homotopy Theory I” (PDF).

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@@ Line 110: / Line 110: @@
 ==memo m==
 <ref>{{cite book |title=Handbook of Algebraic Topology |date=1995 |doi=10.1016/B978-0-444-81779-2.X5000-7 |isbn=978-0-444-81779-2|url=https://ncatlab.org/nlab/files/DwyerSpalinski_HomotopyTheories.pdf }}</ref>
+Wikipedia:Articles for deletion/Associativity isomorphism
+Would you tell me more about no consensus? There seems to be consensus that as a standalone article, it does not meet the [[WP:N]]. Maybe I should have linked to [[WP:CFORK]] in the AfD. Should we discuss merging somewhere other than the AfD? (I thought the consensus was merge.)
 ==Coherence==