Homotopy theory for algebras over polynomial monads
By Michael Batanin, C. Berger. Theory and Applications of Categories, 2013
113 citations recorded by the source corpus.
We study the existence and left properness of transferred model structures for "monoid-like" 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d2f374a63de197548ef312f2b9555c2eaf379542
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In Algebra and Number Theory
- L. Pereira
- P. Bonventre
- Martin Markl
- Jakob Scholbach
- D. Pavlov
- Michael Batanin
- David White
- C. Berger
In Geometry and Topology
- L. Pereira
- P. Bonventre
- Martin Markl
- Jakob Scholbach
- D. Pavlov
- David White
- Michael Batanin
- C. Berger
In Mathematical Physics
- L. Pereira
- P. Bonventre
- Martin Markl
- Jakob Scholbach
- D. Pavlov
- Michael Batanin
- David White
- C. Berger
Citations in the corpus
- Admissibility and rectification of colored symmetric operads (2014, background): “monoidal, symmetroidal, and symmetric flat. The key condition of symmetric h-monoidality is a symmetric strengthening of the h-monoidality condition. The latter was introduced by Batanin and Berger in [BB13] and is closely related to the monoid axiom. Essentially, it means that for any object Y in Σn”
- Genuine equivariant operads (2017, methodology): “2) adapts the key patterns in [50],[2] while focusing on the G-tree perspective for intuition.”
- Operadic categories and Duoidal Deligne's conjecture (2014, methodology): “such as Feynman categories of Kaufmann [24], polynomial monads [6], moment categories of Berger [13] and operator categories of Barwick [2].”
- Model structures on commutative monoids in general model categories (2014, background): “1 in [2], the proof above also has a relative version whenM fails to be h-monoidal.”