Strict 2-toposes

نویسندگان

  • Mark Weber
  • MARK WEBER
چکیده

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the yoneda structure [SW78] it generates are explored. Examples relevant to the globular approach to higher dimensional category theory are discussed. This paper also contains some expository material on the theory of fibrations internal to a finitely complete 2category [Str74b] and provides a self-contained development of the necessary background material on yoneda structures.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Arithmetic universes and classifying toposes

The paper uses structures in Con, the author’s 2-category of sketches for arithmetic universes (AUs), to provide constructive, base-independent results for Grothendieck toposes (bounded S-toposes) as generalized spaces. The main result is to show how an extension map U : T1 → T0 can be viewed as a bundle, transforming base points (models of T0 in any elementary topos S with nno) to fibres (gene...

متن کامل

Molecular Toposes*

In [2], Barr and Diaconescu characterized those Grothendieck toposes 8 for which the inverse image, A, of the geometric morphism r: 8 + Yet, is logical. It was shown (among other things) that this happens precisely when the lattice of subobjects of every object of 8 is a complete atomic boolean algebra. Toposes satisfying this property are called atomic. These results were relativised to the ca...

متن کامل

Cocomplete toposes whose exact completions are toposes

Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere–Schanuel characterization of Boolean presheaf toposes and Hofstra’s characterization of the locally connected Gro...

متن کامل

Partial Toposes Jean Bénabou and Thomas Streicher

We introduce various notions of partial topos, i.e. “topos without terminal object”. The strongest one, called local topos, is motivated by the key examples of finite trees and sheaves with compact support. Local toposes satisfy all the usual exactness properties of toposes but are neither cartesian closed nor have a subobject classifier. Examples for the weaker notions are local homeomorphisms...

متن کامل

Exact completions and toposes

Toposes and quasi-toposes have been shown to be useful in mathematics, logic and computer science. Because of this, it is important to understand the different ways in which they can be constructed. Realizability toposes and presheaf toposes are two important classes of toposes. All of the former and many of the latter arise by adding “good” quotients of equivalence relations to a simple catego...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006