On finiteness spaces and extensional presheaves over the Lawvere theory of polynomials
نویسنده
چکیده
We define a faithful functor from a cartesian closed category of linearly topologized vector spaces over a field and generalized polynomial functions to the category of “extensional” presheaves over the Lawvere theory of polynomial functions, and show that, under some conditions on the field, this functor is full and preserves the cartesian closed structure.
منابع مشابه
Segal Condition Meets Computational Effects
Every finitary monad T on the category of sets is described by an algebraic theory whose n-ary operations are the elements of the free algebra Tn generated by n letters. This canonical presentation of the monad (called its Lawvere theory) offers a precious guideline in the search for an intuitive presentation of the monad by generators and relations. Hence, much work has been devoted to extend ...
متن کاملSound and Complete Equational Reasoning over Comodels
Comodels of Lawvere theories, i.e. models in Set , model state spaces with algebraic access operations. Standard equational reasoning is known to be sound but incomplete for comodels. We give two sound and complete calculi for equational reasoning over comodels: an inductive calculus for equality-on-the-nose, and a coinductive/inductive calculus for equality modulo bisimulation which captures b...
متن کاملCategory and subcategories of (L,M)-fuzzy convex spaces
Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...
متن کاملConvex Spaces I: Definition and Examples
We propose an abstract definition of convex spaces as sets where one can take convex combinations in a consistent way. A priori, a convex space is an algebra over a finitary version of the Giry monad. We identify the corresponding Lawvere theory as the category from [Fri09] and use the results obtained there to extract a concrete definition of convex space in terms of a family of binary operati...
متن کاملA Finiteness Theorem for Canonical Heights Attached to Rational Maps over Function Fields
Let K be a function field, let φ ∈ K(T ) be a rational map of degree d ≥ 2 defined over K, and suppose that φ is not isotrivial. In this paper, we show that a point P ∈ P(K̄) has φ-canonical height zero if and only if P is preperiodic for φ. This answers affirmatively a question of Szpiro and Tucker, and generalizes a recent result of Benedetto from polynomials to rational functions. We actually...
متن کامل