Algebraic weak factorisation systems II: Categories of weak maps
نویسندگان
چکیده
منابع مشابه
Algebraic Weak Factorisation Systems Ii: Categories of Weak Maps
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 “hom...
متن کاملAlgebraic Weak Factorisation Systems I: Accessible Awfs
Algebraic weak factorisation systems (awfs) refine weak factorisation systems by requiring that the assignations sending a map to its first and second factors should underlie an interacting comonad–monad pair on the arrow category. We provide a comprehensive treatment of the basic theory of awfs—drawing on work of previous authors—and complete the theory with two main new results. The first pro...
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Loosely speaking, “homotopy theory” is a perspective which treats objects as equivalent if they have the same “shape” which, for a category theorist, occurs when there exists a certain class W of morphisms that one would like to invert, but which are not in fact isomorphisms. Model categories provide a setting in which one can do “abstract homotopy theory” in subjects far removed from the origi...
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Adhesive high-level replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graph-like structures, various kinds of Petri nets and algebraic high-level (AHL) nets are interesting instantiations of adhesive HLR systems. AHL nets combine algebraic spec...
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Adhesive high-level replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graph-like structures, various kinds of Petri nets and algebraic high-level (AHL) nets are interesting instantiations of adhesive HLR systems. AHL nets combine algebraic spec...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2016
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2015.06.003