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Abstract
We give an example of a morphism of simplicial sets which is a monomorphism, bijective on 0simplices, and a weak categorical equivalence, but which is not inner anodyne. This answers an open question of Joyal. Furthermore, we use this morphism to refute a plausible description of the class of fibrations in Joyal's model structure for quasicategories.
Original language  English 

Pages (fromto)  3740 
Number of pages  4 
Journal  Proceedings of the American Mathematical Society 
Volume  148 
Issue number  1 
Early online date  9 Jul 2019 
DOIs  
Publication status  Published  Jan 2020 
Keywords
 inner anodyne
 quasicategory
 inner fibration
 Weak factorisation system
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Projects
 1 Finished

Monoidal categories and beyond: new contexts and new applications
Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.
30/06/16 → 17/06/19
Project: Research