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math.CT2024★ 1 cited
Templicial nerve of an A-infinity category
Violeta Borges Marques, Arne Mertens
The framework of templicial vector spaces was put forth in arXiv:2302.02484v2 as a suitable generalization of simplicial sets in order to develop a theory of enriched quasi-categor…
math.CT2024
Nerves of enriched categories via necklaces
Arne Mertens
We introduce necklicial nerve functors from enriched categories to simplicial sets, which include Cordier's homotopy coherent, Lurie's differential graded and Le Grignou's cubical…
math.CT2024
Discrete vertices in simplicial objects internal to a monoidal category
Arne Mertens
We follow the work of Aguiar on internal categories and introduce simplicial objects internal to a monoidal category as certain colax monoidal functors. Then we compare three appro…