Dilations of partial representations of Hopf algebras

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory.Comment: 25 pages. Corrected several typos, final version to appear in Journal of the London Mathematical Societ

Gene regulation knowledge commons: community action takes care of DNA binding transcription factors

A large gap remains between the amount of knowledge in scientific literature and the fraction that gets curated into standardized databases, despite many curation initiatives. Yet the availability of comprehensive knowledge in databases is crucial for exploiting existing background knowledge, both for designing follow-up experiments and for interpreting new experimental data. Structured resources also underpin the computational integration and modeling of regulatory pathways, which further aids our understanding of regulatory dynamics. We argue how cooperation between the scientific community and professional curators can increase the capacity of capturing precise knowledge from literature. We demonstrate this with a project in which we mobilize biological domain experts who curate large amounts of DNA binding transcription factors, and show that they, although new to the field of curation, can make valuable contributions by harvesting reported knowledge from scientific papers. Such community curation can enhance the scientific epistemic process.Database URL: http://www.tfcheckpoint.org

Hopf Categories

We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation Theor