منابع مشابه
Exponentiable Streams and Prestreams
Inspired by a construction of Escardó, Lawson, and Simpson, we give a general construction of C-generated objects in a topological construct. When 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 st...
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Given a map f in the category ω-Cpo of ω-complete posets, exponentiability of f in ω-Cpo easily implies exponentiability of f in the category Pos of posets, while the converse is not true. We find then the extra conditions needed on f exponentiable in Pos to be exponentiable in ω-Cpo, showing the existence of partial products of the two-point ordered set S = {0 < 1} (Theorem 1.8). Using this ch...
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A categorical proof of the statement given by the title is provided, in generalization of a result for topological spaces proved recently by Clementino, Hofmann and Tholen.
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Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey some lax commutativity; this, in turn, is precisely what is needed to prove the existence of partial products with that functor; so that the functor’s expone...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2013
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-013-9315-x