This paper is a coalgebra version of Positselski (Rendiconti Seminario Matematico Univ.
Padova 143: 153–225, 2020) and a sequel to Positselski (Algebras and Represent Theory …

We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent
coassociative coalgebras CC and D D. Given such a complex ℬ∙ B^∙, we construct an …

We define $ A_ {\infty} $-structures--algebras, coalgebras, modules, and comodules--in an
arbitrary monoidal DG category or bicategory by rewriting their definitions in terms of …

Chapter 2 sets the definitions of our objects of studies: coalgebras and their comodules, both
in the ordinary sense and in the∞-categorical sense. Our main result here is Proposition 2.2 …

The construction of the cotensor coalgebra for an “abelian monoidal” category M which is
also cocomplete, complete and AB5, was performed in Ardizzoni et al.(Comm Algebra 35 …

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in
an Abelian monoidal category ℳ. If ℳ is also cocomplete, complete, and AB5, we show that …

We characterize in bicategorical terms actions of monoidal categories on the categories of
representations of algebras and of relative Hopf modules. For this purpose we introduce 2 …

A monoidal (or tensor) category consists of a category M which is endowed with a
distinguished object 1 (called unit) and with a functor⊗: M× M→ M (called tensor product) …

We use Lurie's symmetric monoidal envelope functor to give two new descriptions of∞-
operads: as certain symmetric monoidal∞-categories whose underlying symmetric …

Consider a monoidal category that is at the same time abelian with enough projectives and
such that projectives are flat on the right. We show that there is a-algebra that is-quasi …