Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative injectivity as cocompleteness for a class of distributors   Notions and techniques of enriched category theory can be used to study
topological structures, like metric spaces, topological spaces and approach
spaces, in the context of topological theories. Recently in [D. Hofmann,
Injective spaces via adjunction, arXiv:0804.0326 [math.CV]] the construction of
a Yoneda embedding allowed to identify injectivity of spaces as cocompleteness
and to show monadicity of the category of injective spaces and left adjoints
over $\mathsf{Set}$. In this paper we generalise these results, studying
cocompleteness with respect to a given class of distributors. We show in
particular that the description of several semantic domains presented in [M.
Escard\'o and B. Flagg, Semantic domains, injective spaces and monads,
Electronic Notes in Theoretical Computer Science 20 (1999)] can be translated
into the $\mathsf{V}$-enriched setting.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat