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∞-Categories for the Working Mathematician
homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,
Traced monoidal categories
Traced monoidal categories are introduced, a structure theorem is proved for them, and an example is provided where the structure theorem has application.
Complicial sets characterising the simplicial nerves of strict ω-categories
Simplicial operators and simplicial sets A little categorical background Double categories, 2-categories and $n$-categories An introduction to the decalage construction Stratifications and filterings
The theory and practice of Reedy categories
The goal of this paper is to demystify the role played by the Reedy category axioms in homotopy theory by reducing the much of the hard work involved to simpler computations involving weighted colimits and Leibniz (pushout-product) constructions.
Elements of ∞-Category Theory
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an