Localized dg-coalgebras over a field are equivalent to coalgebras over cofibrant enriched ∞-operads via induction on cell attachments, yielding point-set models for E_n-coalgebras and cellular chains.
Cofree coalgebras over operads and representative functions
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We give a recursive formula to compute the cofree coalgebra P^\vee(C) over any colored operad P in Set, CGHaus or (dg)Vect. The construction is closed to that of Smith but different. We use a more conceptual approach to simplify the proofs that P^\vee is the cofree P-coalgebra functor and also the comonad generating P-coalgebras. In a second part, when P is a linear or dg-operad over a field, we generalize the notion of representative functions of Block & Leroux and prove that P^\vee(C) is simply the subobject of representative elements in the "completed P-algebra" P^\wedge(C). This says that our recursion (as well as that of Smith) stops at the first step.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Enriched coalgebras over unital operads in semicartesian V-categories are the coalgebras of a constructed V-comonad.
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Point-set models for homotopy coherent coalgebras
Localized dg-coalgebras over a field are equivalent to coalgebras over cofibrant enriched ∞-operads via induction on cell attachments, yielding point-set models for E_n-coalgebras and cellular chains.
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Enriched coalgebras are sometimes comonadic
Enriched coalgebras over unital operads in semicartesian V-categories are the coalgebras of a constructed V-comonad.