3 citations · 5 across the 7 of their papers we have counts for
8 papers
The category of necklaces is a test category
Arne Mertens
In this short note, we prove that the category of necklaces is a test category. Hence presheaves on necklaces model homotopy types. The proof is analogous to that for the category…
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…
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…
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…
Deformations of quasi-categories in modules
Violeta Borges Marques, Wendy Lowen, Arne Mertens
The framework of templicial objects was put forth in arXiv:2302.02484v1 in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categori…
The category of necklaces is Reedy monoidal
Violeta Borges Marques, Arne Mertens
In the first part of this note we further the study of the interactions between Reedy and monoidal structures on a small category, building upon the work of Barwick. We define a Re…
Enriched quasi-categories and the templicial homotopy coherent nerve
Wendy Lowen, Arne Mertens
We lay the foundations for a theory of quasi-categories in a monoidal category replacing , aimed at realising weak enrichment in the category $S\mathcal…
Frobenius templicial modules and the dg-nerve
Wendy Lowen, Arne Mertens
Templicial objects were put forth in arXiv:2302.02484v2 to set up a suitable simplicial framework for enriched quasi-categories. Following Leinster, these objects feature certain c…