Minimal models for graph-related (hyper)operads

We construct explicit minimal models for the (hyper)operads governing modular, cyclic and ordinary operads, and wheeled properads, respectively. Algebras for these models are homotopy versions of the corresponding structures.     

Cotorsion Pairs and Stable Categories over Triangular Matrix Rings北大核心CSCD

In general, the properties of modules over a triangular matrix ring T = (0ABU) are studied via modules over diagonal “small rings” A and B. However, we use model structures on the category of T-modules to characterize the stable categories GP(A), GP(B) of Gorenstein projective modules over A and B. To this end, we introduce two subcategories of Gorenstein T-modules, and obtain two corresponding complete cotorsion pairs. Moreover, cotorsion pairs of modules are lifted to T-complexes, and the equivalences and recollements of homotopy categories of complexes are studied. © 2022 Chinese Academy of Sciences. All rights reserved.     

Geometric partial comodules over flat coalgebras in Abelian categories are globalizable

The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial representations of groups and Hopf algebras, our globalization coincides with those described earlier in literature. Finally, we introduce Hopf partial comodules over a bialgebra as geometric partial comodules in the monoidal category of (global) modules. By applying our globalization theorem we obtain an analogue of the fundamental theorem for Hopf modules in this partial setting.