Operads without coalgebras
Brice Le Grignou, Damien Lejay
TL;DR
This paper presents an example of a linear operad with only trivial coalgebras and discusses conditions for the cofree coalgebra functor to be faithful, contributing to the understanding of operad-coalgebra relationships.
Contribution
It introduces a non-trivial linear operad with trivial coalgebras and provides conditions for faithfulness of the cofree coalgebra functor.
Findings
Existence of a non-trivial operad with only trivial coalgebras
Conditions for the faithfulness of the cofree coalgebra functor
Insights into operad and coalgebra structures
Abstract
We give an example of a non-trivial linear operad that only admits trivial coalgebras and give sufficient conditions ensuring that the cofree coalgebra functor be faithful.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models