Coextension of scalars in operad theory

Gabriel C. Drummond-Cole; Philip Hackney

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Coextension of scalars in operad theory

Gabriel C. Drummond-Cole, Philip Hackney

Category Theory · Submitted 28 Jun 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give a necessary and sufficient condition for the restriction functor to admit a right adjoint.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,919 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.23 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The functor between operadic algebras given by restriction along an operad map generally has a left adjoint.	background 0.99	0.10	0.10	asserted 0.93
s1	We give a necessary and sufficient condition for the restriction functor to admit a right adjoint.	contribution 0.51	0.94	0.55	asserted 1.00
s2	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.	result 0.77	0.82	0.53	asserted 0.97

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

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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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 4 sentences without a confident label

Compares with 2 papers

In the colored setting, a version of this exceptional right adjoint appears, more or less, as the subcategory inclusion in [ref] .

Dwyer--Kan homotopy theory for cyclic operads · The general case · 0.81
When $= =$, Definition [ref] agrees with the colored circle product $∘$ from [ref] , the colored symmetric circle product $∘^𝖲$ from [ref] , and the $$-product from [ref] .

Infinity Operads and Monoidal Categories with Group Equivariance · Collections · 0.97

Cites as background 1 paper

Alternative presentations of such graphs may be found in [ref] , [ref] , and [ref] .

Modular operads and the nerve theorem · Examples of colored operads · 0.96

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