A notion of homotopy for the effective topos
نویسنده
چکیده
We define a notion of homotopy in the effective topos. AMS Subject Classification (2000): 18B25 (Topos Theory),55U35 (Abstract and axiomatic homotopy theory)
منابع مشابه
A homotopy-theoretic model of function extensionality in the effective topos
We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σand Π-types, a...
متن کاملAxioms for Modelling Cubical Type Theory in a Topos
The homotopical approach to intensional type theory views proofs of equality as paths. We explore what is required of an interval-like object I in a topos to give a model of type theory in which elements of identity types are functions with domain I. Cohen, Coquand, Huber and Mörtberg give such a model using a particular category of presheaves. We investigate the extent to which their model con...
متن کاملTopos based homology theory
In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the...
متن کاملOn Constructive Axiomatic Method
The formal axiomatic method popularized by Hilbert and recently defended by Hintikka is not fully adequate to the recent practice of axiomatizing mathematical theories. The axiomatic architecture of Topos theory and Homotopy type theory do not fit the pattern of the formal axiomatic theory in the standard sense of the word. However these theories fall under a more general and in some respects m...
متن کاملInternal Universes in Models of Homotopy Type Theory
We show that universes of fibrations in various models of homotopy type theory have an essentially global character: they cannot be described in the internal language of the presheaf topos from which the model is constructed. We get around this problem by extending the internal language with a modal operator for expressing properties of global elements. In this setting we show how to construct ...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 25 شماره
صفحات -
تاریخ انتشار 2015