Small Bialgebras with a Projection: Applications

In this paper we continue the investigation started in [A.M.St.-Small], dealing with bialgebras $A$ with an $H$-bilinear coalgebra projection over an arbitrary subbialgebra $H$ with antipode. These bialgebras can be described as deformed bosonizations R#_{\xi} H of a pre-bialgebra $R$ by $H$ with a cocycle $\xi$. Here we describe the behavior of $\xi$ in the case when $R$ is f.d. and thin i.e. it is connected with one dimensional space of primitive elements. This is used to analyze the arithmetic properties of $A$. Meaningful results are obtained when $H$ is cosemisimple. By means of Ore extension construction, we provide some examples of atypical situations (e.g. the multiplication of $R$ is not $H$-colinear or $\xi$ is non-trivial)

Categories of comodules and chain complexes of modules

Let \lL(A) denote the coendomorphism left $R$-bialgebroid associated to a left finitely generated and projective extension of rings $R \to A$ with identities. We show that the category of left comodules over an epimorphic image of \lL(A) is equivalent to the category of chain complexes of left $R$-modules. This equivalence is monoidal whenever $R$ is commutative and $A$ is an $R$-algebra. This is a generalization, using entirely new tools, of results by B. Pareigis and D. Tambara for chain complexes of vector spaces over fields. Our approach relies heavily on the non commutative theory of Tannaka reconstruction, and the generalized faithfully flat descent for small additive categories, or rings with enough orthogonal idempotents.Comment: The title has been changed, the first part is removed and the construction of the coendomorphim bialgebroid is now freely used in the statement of the main Theorem

Noninteracting control with stability for Hamiltonian systems

Published versio

Braided Bialgebras of Type One

Braided bialgebras of type one in abelian braided monoidal categories are characterized as braided graded bialgebras which are strongly $\mathbb{N}$-graded both as an algebra and as a coalgebra

Cotensor Coalgebras in Monoidal Categories

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal property. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth

Pre-torsors and Galois comodules over mixed distributive laws

We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions $(N_A,R_A)$ and $(N_B,R_B)$ on one hand, and the category of regular comonad arrows $(R_A,\xi)$ from some equalizer preserving comonad ${\mathbb C}$ to $N_BR_B$ on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of coalgebras.Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad ${\mathbb D}$ and a co-regular comonad arrow from ${\mathbb D}$ to $N_A R_A$, such that the comodule categories of ${\mathbb C}$ and ${\mathbb D}$ are equivalent.Comment: 34 pages LaTeX file. v2: a few typos correcte

Increased tumor necrosis factor alpha-converting enzyme activity induces insulin resistance and hepatosteatosis in mice

Tumor necrosis factor alpha-converting enzyme (TACE, also known as ADAM17) was recently involved in the pathogenesis of insulin resistance. We observed that TACE activity was significantly higher in livers of mice fed a high-fat diet (HFD) for 1 month, and this activity was increased in liver > white adipose tissue > muscle after 5 months compared with chow control. In mouse hepatocytes, C(2)C(12) myocytes, and 3T3F442A adipocytes, TACE activity was triggered by palmitic acid, lipolysaccharide, high glucose, and high insulin. TACE overexpression significantly impaired insulin-dependent phosphorylation of AKT, GSK3, and FoxO1 in mouse hepatocytes. To test the role of TACE activation in vivo, we used tissue inhibitor of metalloproteinase 3 (Timp3) null mice, because Timp3 is the specific inhibitor of TACE and Timp3(-/-) mice have higher TACE activity compared with wild-type (WT) mice. Timp3(-/-) mice fed a HFD for 5 months are glucose-intolerant and insulin-resistant; they showed macrovesicular steatosis and ballooning degeneration compared with WT mice, which presented only microvesicular steatosis. Shotgun proteomics analysis revealed that Timp3(-/-) liver showed a significant differential expression of 38 proteins, including lower levels of adenosine kinase, methionine adenosysltransferase I/III, and glycine N-methyltransferase and higher levels of liver fatty acid-binding protein 1. These changes in protein levels were also observed in hepatocytes infected with adenovirus encoding TACE. All these proteins play a role in fatty acid uptake, triglyceride synthesis, and methionine metabolism, providing a molecular explanation for the increased hepatosteatosis observed in Timp3(-/-) compared with WT mice. Conclusion: We have identified novel mechanisms, governed by the TACE-Timp3 interaction, involved in the determination of insulin resistance and liver steatosis during overfeeding in mice

Anion and cation permeability of the mouse tmem16f calcium-activated channel

TMEM16F is involved in several physiological processes, such as blood coagulation, bone development and virus infections. This protein acts both as a Ca2+-dependent phospholipid scram-blase and a Ca2+-activated ion channel but several studies have reported conflicting results about the ion selectivity of the TMEM16F-mediated current. Here, we have performed a detailed side-by-side comparison of the ion selectivity of TMEM16F using the whole-cell and inside-out excised patch configurations to directly compare the results. In inside-out configuration, Ca2+-dependent activation was fast and the TMEM16F-mediated current was activated in a few milliseconds, while in whole-cell recordings full activation required several minutes. We determined the relative permeability between Na+ and Cl¯ (PNa /PCl ) using the dilution method in both configurations. The TMEM16F-mediated current was highly nonselective, but there were differences depending on the configuration of the recordings. In whole-cell recordings, PNa /PCl was approximately 0.5, indicating a slight preference for Cl¯ permeation. In contrast, in inside-out experiments the TMEM16F channel showed a higher permeability for Na+ with PNa /PCl reaching 3.7. Our results demonstrate that the time dependence of Ca2+ activation and the ion selectivity of TMEM16F depend on the recording configuration