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Metric enrichment, finite generation, and the path coreflection

Alexandru Chirvasitu (2024)

Archivum Mathematicum

We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally ℵ 1 -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry- ℵ 0 -generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include...

On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions

Hans-Jürgen Vogel (2001)

Discussiones Mathematicae - General Algebra and Applications

The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family d = ( d A : A → A ⨂ A | A ∈ | R e l | ) of diagonal morphisms, a family t = ( t A : A → I | A ∈ | R e l | ) of terminal morphisms, and a family ∇ = ( ∇ A : A ⨂ A → A | A ∈ | R e l | ) of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....

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