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

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

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

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

In vitro evaluation of antiviral and virucidal activity of a high molecular weight hyaluronic acid.

BACKGROUND: hyaluronic acid (HA), a non-sulphated glycosaminoglycan, is present in synovial fluid, vitreous humour serum and many connective tissues. Pharmaceutical preparations of HA are used in clinical practice for wound healing, joint pain, kerato-conjunctivitis, asthma, mouth care, oesophageal-reflux, and gastritis. Moreover, it is used as a filler to counteract ageing and facial lipoatrophy. Our study aims at investigating the in vitro antiviral activity of a high molecular weight HA.METHODS: the MTT test was used to rule out the potential toxic effects of HA on the different cell lines used in the antiviral assays. The antiviral activity of HA against Coxsackievirus B5, Herpes simplex virus-1, Mumps virus, Adenovirus-5, Influenza Virus A/H1N1, Human Herpesvirus-6, Porcine Parvovirus, Porcine Reproductive and Respiratory Syndrome Virus was assessed by virus yield assays.RESULTS: the most effective inhibition was observed against Coxsackievirus B5, with 3Log reduction of the virus yield at 4mg/ml, and a reduction of 3.5Log and 2Log, at 2mg/ml and 1mg/ml, respectively: the selectivity index was 16. Mumps virus was highly inhibited too showing a reduction of 1.7Log at 1mg/ml and 1Log at 4mg/ml and 2mg/ml (selectivity index = 12). The selectivity index for Influenza Virus was 12 with the highest inhibition (1Log) observed at 4mg/ml. Herpes simplex virus-1 and Porcine Parvovirus were mildly inhibited, whereas no antiviral activity was observed with respect to Adenovirus-5, Human Herpesvirus-6, Porcine Reproductive and Respiratory Syndrome Virus. No HA virucidal activity was ever observed against any of the viruses tested. Kinetic experiments showed that both Coxsackievirus B5 and Herpes simplex virus-1 replication were consistently inhibited, not influenced by the time of HA addition, during the virus replication cycle.CONCLUSIONS: the spectrum of the antiviral activity exhibited by HA against both RNA and DNA viruses, known to have different structures (with or without envelope) and replication strategies, suggests a non specific mechanism of action, probably involving cell membrane-virus interaction steps. The results of the kinetic experiments support this hypothesis