کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897389 | 1630739 | 2018 | 45 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Exact completion of path categories and algebraic set theory
ترجمه فارسی عنوان
تکمیل دقیق مقوله های مسیر و نظریه مجموعه جبری
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We introduce the notion of a “category with path objects”, as a slight strengthening of Kenneth Brown's classical notion of a “category of fibrant objects”. We develop the basic properties of such a category and its associated homotopy category. Subsequently, we show how the exact completion of this homotopy category can be obtained as the homotopy category associated to a larger category with path objects, obtained by freely adjoining certain homotopy quotients. In a second part of this paper, we will present an application to models of constructive set theory. Although our work is partly motivated by recent developments in homotopy type theory, this paper is written purely in the language of homotopy theory and category theory, and we do not presuppose any familiarity with type theory on the side of the reader.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 10, October 2018, Pages 3137-3181
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 10, October 2018, Pages 3137-3181
نویسندگان
Benno van den Berg, Ieke Moerdijk,