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Exponentiable Streams and Prestreams

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Abstract

Inspired by a construction of Escardó, Lawson, and Simpson, we give a general construction of \(\mathcal C\)-generated objects in a topological construct. When \(\mathcal C\) consists of exponentiable objects, the resulting category is Cartesian-closed. This generalizes the familiar construction of compactly-generated spaces, and we apply this to Krishnan’s categories of streams and prestreams, as well as to Haucourt streams. For that, we need to identify the exponentiable objects in these categories: for prestreams, we show that these are the preordered core-compact topological spaces, and for streams, these are the core-compact streams.

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Authors and Affiliations

  1. ENS Cachan, 61 avenue du président Wilson, 94230, Cachan, France

    Jean Goubault-Larrecq

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  1. Jean Goubault-Larrecq
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Correspondence to Jean Goubault-Larrecq.

Additional information

This work was inspired by a talk given by Sanjeevi Krishnan at Dagstuhl seminar 10232 “The Semantics of Information”, June 2010.

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Goubault-Larrecq, J. Exponentiable Streams and Prestreams. Appl Categor Struct 22, 515–549 (2014). https://doi.org/10.1007/s10485-013-9315-x

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  • DOI: https://doi.org/10.1007/s10485-013-9315-x

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