Titlebook: Effective Kan Fibrations in Simplicial Sets; Benno van den Berg,Eric Faber Book 2022 The Editor(s) (if applicable) and The Author(s), unde

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PreliminariesIn this chapter we introduce the main theoretical framework in which our theory of effective fibrations is embedded. Abstractly put, we are studying and constructing new notions of . and . on a category ..

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Simplicial Sets as a Symmetric Moore CategoryIn this chapter we equip the category of simplicial with the structure of a symmetric Moore category. For this we use the simplicial Moore path functor originally defined by Clemens Berger, Richard Garner and the first author.

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Mould Squares in Simplicial SetsIn this chapter we embark on the study of the effective Kan fibrations in simplicial sets defined using the dominance and symmetric Moore structure on simplicial sets that we established in the previous chapters. The main result of this chapter is that these effective Kan fibrations are cofibrantly generated by a small triple category.

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ConclusionIn this final chapter we would like to take stock of the properties of effective Kan fibrations that we have established and outline some directions for future research.

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https://doi.org/10.1007/978-3-658-17888-8 factorisation system will be shown to be the class of . defined by the dominance, while the right class (algebras) is called the class of .. Proposition . can also be found in Bourke and Garner [.]. The rest of the chapter studies the (double) category of effective cofibrations a bit more closely a