Projects per year
Abstract
We study the existence and left properness of transferred model structures for “monoidlike” objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular, higher operads, properads and PROP’s. All these structures can be realised as algebras over polynomial monads. We give a general condition for a polynomial monad which ensures the existence and (relative) left properness of a transferred model structure for its algebras. This condition is of a combinatorial nature and singles out a special class of polynomial monads which we call tame polynomial. Many important monads are shown to be tame polynomial.
Original language  English 

Pages (fromto)  148253 
Number of pages  106 
Journal  Theory and Applications of Categories 
Volume  32 
Issue number  6 
Publication status  Published  6 Feb 2017 
Keywords
 quillen model category
 polynomial monad
 coloured operad
 graph
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Projects
 1 Finished

Enriched higher category theory
Batanin, M., Markl, M., Berger, C. & MQRES, M.
1/01/13 → 31/12/16
Project: Research