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{{cite arXiv |last1=Schreiber |first1=Urs |last2=Škoda |first2=Zoran |title=Categorified symmetries |date=2010 |class=math.QA |eprint=1004.2472 }} |
{{cite arXiv |last1=Schreiber |first1=Urs |last2=Škoda |first2=Zoran |title=Categorified symmetries |date=2010 |class=math.QA |eprint=1004.2472 }} |
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Latest revision as of 16:41, 21 September 2025
https://books.google.com/books?id=okHfUv4l4vgC&pg=PA57
[1]
- 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.
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- N a t ( A ( A , − ) , F ) ≅ F ( A ) . {\displaystyle \mathrm {Nat} ({\mathcal {A}}(A,-),F)\cong F(A).}
α h , g , f : ( h ∘ g ) ∘ f → ≅ h ∘ ( g ∘ f ) {\displaystyle \alpha _{h,g,f}:(h\circ g)\circ f{\stackrel {\cong }{\to }}h\circ (g\circ f)}
- 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.
- 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.
- 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.
- 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.
- 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.
Beck’s monadicity theorem for ∞-category
[edit]
a fully faithful and essentially surjective functor is an equivalence for precategories
[edit]
Ahrens, Benedikt; Paige Randall North; Shulman, Michael; Tsementzis, Dimitris (2021). “The Univalence Principle (3.2. Categories in HoTT)”. arXiv:2102.06275 [math.CT].
- ^ Costa, Laura; Miró-Roig, Rosa María; Pons-Llopis, Joan (2021). Ulrich Bundles. doi:10.1515/9783110647686. ISBN 9783110647686.
- ^ 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.
- ^ Kahn, Bruno (2025). “On the Bénabou-Roubaud theorem” (PDF). Cahiers de topologie et géométrie différentielle catégoriques. LXVI (2): 3–12. arXiv:2404.00868.
- ^ Lurie, Jacob (2003). “On Infinity Topoi”. arXiv:math/0306109.
- ^ 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.
