11,403 research outputs found
On the Largest Cartesian Closed Category of Stable Domains
AbstractLet SABC (resp., SABC˜) be the category of algebraic bounded complete domains with conditionally multiplicative mappings, that is, Scott-continuous mappings preserving meets of pairs of compatible elements (resp., stable mappings). Zhang showed that the category of dI-domains is the largest cartesian closed subcategory of ω-SABC and ω-SABC˜, with the exponential being the stable function space, where ω-SABC and ω-SABC˜ are full subcategories of SABC and SABC˜ respectively which contain countablly based algebraic bounded complete domains as objects. This paper shows that:i)The exponentials of any full subcategory of SABC or SABC˜ are exactly function spaces;ii)SDABC˜ the category of distributive algebraic bounded complete domains, is the largest cartesian closed subcategory of SABC˜; The compact elements of function spaces in the category SABC are also studied
On Linear Information Systems
Scott's information systems provide a categorically equivalent, intensional
description of Scott domains and continuous functions. Following a well
established pattern in denotational semantics, we define a linear version of
information systems, providing a model of intuitionistic linear logic (a
new-Seely category), with a "set-theoretic" interpretation of exponentials that
recovers Scott continuous functions via the co-Kleisli construction. From a
domain theoretic point of view, linear information systems are equivalent to
prime algebraic Scott domains, which in turn generalize prime algebraic
lattices, already known to provide a model of classical linear logic
D-modules on Spaces of Rational Maps and on other Generic Data
Let X be an algebraic curve. We study the problem of parametrizing geometric
data over X, which is only generically defined. E.g., parametrizing generically
defined (aka rational) maps from X to a fixed target scheme Y. There are three
methods for constructing functors of points for such moduli problems (all
originally due to Drinfeld), and we show that the resulting functors are
equivalent in the fppf Grothendieck topology. As an application, we obtain
three presentations for the category of D-modules "on" B (K) \G (A) /G (O), and
we combine results about this category coming from the different presentations.Comment: 55 page
Categories of embeddings
AbstractWe present a categorical generalisation of the notion of domains, which is closed under (suitable) exponentiation. The goal was originally to generalise Girard's model of polymorphism to Fω. If we specialise this notion in the poset case, we get new cartesian closed categories of domains
Algebraic Kasparov K-theory. I
This paper is to construct unstable, Morita stable and stable bivariant
algebraic Kasparov -theory spectra of -algebras. These are shown to be
homotopy invariant, excisive in each variable -theories. We prove that the
spectra represent universal unstable, Morita stable and stable bivariant
homology theories respectively.Comment: This is the final revised versio
A General Framework for the Semantics of Type Theory
We propose an abstract notion of a type theory to unify the semantics of
various type theories including Martin-L\"{o}f type theory, two-level type
theory and cubical type theory. We establish basic results in the semantics of
type theory: every type theory has a bi-initial model; every model of a type
theory has its internal language; the category of theories over a type theory
is bi-equivalent to a full sub-2-category of the 2-category of models of the
type theory
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