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The Glueing Construction and Double Categories

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arxiv 1112.1307 v1 pith:L5MPGN3F submitted 2011-12-06 math.CT math.GN

Susan Niefield This is my paper · ORCID
classification math.CTmath.GN
keywords categoriesclosedglueinginclusionslocallyartin-wraithdoubleappropriate
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We introduce Artin-Wraith glueing and locally closed inclusions in double categories. Examples include locales, toposes, topological spaces, categories, and posets. With appropriate assumptions, we show that locally closed inclusions are exponentiable, and the exponentials are constructed via Artin-Wraith glueing. Thus, we obtain a single theorem establishing the exponentiability of locally closed inclusions in these five cases.

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  1. Morphisms and comorphisms of sites I -- Double categories of sites

    math.CT 2025-05 conditional novelty 6.0 of 10

    Morphisms and comorphisms of sites become the horizontal and vertical arrows of a double category, sent by sheafification to topoi, with a covers comonad explaining both classes as lax and colax coalgebra morphisms.

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