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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Published in:Mathematische Zeitschrift 2022, Vol.301 (1), p.275-314
Main Authors: Drummond-Cole, Gabriel C., Hackney, Philip
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Language:English
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Mathematics
Mathematics and Statistics
Scalars
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Hackney, Philip
description 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.
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subjects Mathematics
Mathematics and Statistics
Scalars
title Coextension of scalars in operad theory
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