کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415760 1336143 2016 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Algebraic weak factorisation systems II: Categories of weak maps
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Algebraic weak factorisation systems II: Categories of weak maps
چکیده انگلیسی

We investigate the categories of weak maps associated to an algebraic weak factorisation system (awfs) in the sense of Grandis-Tholen [14]. For any awfs on a category with an initial object, cofibrant replacement forms a comonad, and the category of (left) weak maps associated to the awfs is by definition the Kleisli category of this comonad. We exhibit categories of weak maps as a kind of “homotopy category”, that freely adjoins a section for every “acyclic fibration” (= right map) of the awfs; and using this characterisation, we give an alternate description of categories of weak maps in terms of spans with left leg an acyclic fibration. We moreover show that the 2-functor sending each awfs on a suitable category to its cofibrant replacement comonad has a fully faithful right adjoint: so exhibiting the theory of comonads, and dually of monads, as incorporated into the theory of awfs. We also describe various applications of the general theory: to the generalised sketches of Kinoshita-Power-Takeyama [22], to the two-dimensional monad theory of Blackwell-Kelly-Power [4], and to the theory of dg-categories [19].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 220, Issue 1, January 2016, Pages 148-174
نویسندگان
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