CAUTION: The Sender of this email is not from within Dalhousie. [Note from moderator: resending, subject line was inadvertently omitted.] This book is being published, and scheduled for March 2021: M. Grandis Manifolds and Local Structures. A general theory World Scientific Publishing Co., xii + 361 pages, 2021. - Info at WS: https://www.worldscientific.com/worldscibooks/10.1142/12199 - Downloadable Introduction https://www.worldscientific.com/doi/epdf/10.1142/9789811234002_0001 ________ Local structures are studied as symmetric enriched categories on ordered categories of partial morphisms; their morphisms are defined as 'compatible profunctors'. This follows a line presented and developed in 1988-90 (whose main sources are cited in the Preface, below): - MG, Manifolds as enriched categories, in: 'Categorical Topology', Prague 1988, pp.358-368, World Scientific Publishing Co., 1989. - MG, Cohesive categories and manifolds, Ann. Mat. Pura Appl. 157 (1990), 199-244. Downloadable: https://link.springer.com/article/10.1007/BF01765319 The main basis of enrichment is called a 'cohesive e-category', or 'e-category' for short. Later, this structure has been re-introduced under the name of 'restriction category' and equivalent axioms. ________ from the PREFACE Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework. An 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on. This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus. Technically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings. This approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis. ________ Marco Grandis [For admin and other information see: http://www.mta.ca/~cat-dist/ ]