Set Coverings and Invertibility of Functional Galois Connections
نویسندگان
چکیده
We consider equations of the form Bf = g, where B is a Galois connection between lattices of functions. This includes the case where B is the Fenchel transform, or more generally a Moreau conjugacy. We characterize the existence and uniqueness of a solution f in terms of generalized subdifferentials, which extends K. Zimmermann’s covering theorem for max-plus linear equations, and give various illustrations.
منابع مشابه
ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS
Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...
متن کاملA Higher Atiyah–Patodi–Singer Index Theorem for the Signature Operator on Galois Coverings
Let (N, g) be a closed Riemannian manifold of dimension 2m − 1 and let 0→ Ñ → N be a Galois covering of N . We assume that 0 is of polynomial growth with respect to a word metric and that 1Ñ is L 2-invertible in degree m. By employing spectral sections with a symmetry property with respect to the ?-Hodge operator, we define the higher eta invariant associated with the signature operator on Ñ , ...
متن کاملInvertibility of Functional Galois Connections
a INRIA, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France. E-mail: [email protected] b INRIA, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France. E-mail: [email protected] c Dep. of Computing and Mathematics, Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, UK, and Institute for Information Transmission Problems of Russian Academy of Science...
متن کاملGalois coverings of weakly shod algebras
We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomolog...
متن کاملCoverings of Laura Algebras: the Standard Case
In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, has a standard connecting component), then it has Galois coverings associated to the coverings of the connecting component. As a consequence, the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.
متن کامل