A tangent category is a equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of bundle functor from classical differential geometry. Cockett and Cruttwell introduced bundles in 2017 as algebraic alternative to vector arbitrary category. In this paper, we prove smooth manifolds are precisely bundles. particular, means can give characterisation exhibits...

We study the algebraic closure of \(\mathbb {K}(\!(x)\!)\), field power series in several indeterminates over a {K}\). In characteristic zero we show that elements {K}(\!(x)\!)\) can be expressed as Puiseux such convex hull its support is essentially polyhedral rational cone, strengthening known results. positive construct closed fields containing and give examples showing results proved are no...

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

Let Γ be a structure with a finite relational signature and a first-order definition in (R; ∗,+) with parameters from R, that is, a relational structure over the real numbers where all relations are semi-algebraic sets. In this article, we study the computational complexity of constraint satisfaction problem (CSP) for Γ: the problem to decide whether a given primitive positive sentence is true ...