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arxiv: math/9904039 · v1 · submitted 1999-04-09 · 🧮 math.CT · math.AT

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Joins for (Augmented) Simplicial Sets

P.J. Ehlers , T. Porter
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keywords simplicialaugmentedjoinsetsbasecategoryclassicalcomes
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We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.

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  1. Combinatorial Models for Linear Homotopy Theories

    math.AT 2026-05 unverdicted novelty 5.0

    Semisimplicial and augmented semisimplicial modules are equivalent to chain-complex homotopy theories at localization and Quillen levels, while semicubical modules induce a Quillen adjunction but not equivalence due t...