Coextension of scalars in operad theory

The functor between operadic algebras given by restriction along an operad map generally has a left adjoint. We give a necessary and sufficient condition for the restriction functor to admit a right adjoint. The condition is a factorization axiom which roughly says that operations in the codomain op...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2022, Vol.301 (1), p.275-314
Main Authors: Drummond-Cole, Gabriel C., Hackney, Philip
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Scalars
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Summary:The functor between operadic algebras given by restriction along an operad map generally has a left adjoint. We give a necessary and sufficient condition for the restriction functor to admit a right adjoint. The condition is a factorization axiom which roughly says that operations in the codomain operad can be written essentially uniquely as operations in arity one followed by operations in the domain operad.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-021-02840-5