Lax Diagrams and Enrichment

Hugo V. Bacard

Lax Diagrams and Enrichment

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arxiv 1206.3704 v1 pith:PS7PZCLT submitted 2012-06-16 math.CT math.AT

Hugo V. Bacard This is my paper · ORCID

classification math.CTmath.AT

keywords categoriesdefinitionenrichedmodelstructurealternativecalledcategory

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We introduce a new type of weakly enriched categories over a given symmetric monoidal model category M; these are called Co-Segal categories. Their definition derives from the philosophy of classical (enriched) Segal categories. We study their homotopy theory by giving a model structure on them. One of the motivations of introducing these structure was to have an alternative definition of higher linear categories following Segal-like methods.

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The category of necklaces is a test category
math.CT 2026-07 accept novelty 6.0 of 10

The category of necklaces is a test category, so its presheaf category is a model for homotopy types.

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