Exponentiable approach spaces

Hofmann, Dirk; Seal, Gavin J.

doi:10.48550/arxiv.1304.6862

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2020

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“…In Section 2 we introduce (T, V )-categories and list their properties used throughout the paper. In Section 3 we revisit the exponentiability problem in (T, V )-Cat, establishing a sufficient criterion for exponentiability which generalizes the results obtained in [Hof07,HS15]. In Section 4 we study the properties of injective (T, V )-categories which will be used in the forthcoming section to conclude that, under suitable assumptions, injective (T, V )-categories are exponentiable (Theorem 5.8).…”

Section: Introductionmentioning

confidence: 96%

Cartesian closed exact completions in topology

Clementino

Hofmann

Ribeiro

2020

Journal of Pure and Applied Algebra

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Using generalized enriched categories, in this paper we show that Rosický's proof of cartesian closedness of the exact completion of the category of topological spaces can be extended to a wide range of topological categories over Set, like metric spaces, approach spaces, ultrametric spaces, probabilistic metric spaces, and bitopological spaces. In order to do so we prove a sufficient criterion for exponentiability of (T, V )-categories and show that, under suitable conditions, every injective (T, V )-category is exponentiable in (T, V )-Cat.

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Section: Introductionmentioning

confidence: 96%