Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fullness Axiom and exact completion of homotopy categories   We use a category-theoretic formulation of Aczel's Fullness Axiom from
Constructive Set Theory to derive the local cartesian closure of an exact
completion. As an application, we prove that such a formulation is valid in the
homotopy category of any model category satisfying mild requirements, thus
obtaining in particular the local cartesian closure of the exact completion of
topological spaces and homotopy classes of maps. Under a type-theoretic
reading, these results provide a general motivation for the local cartesian
closure of the category of setoids. However, results and proofs are formulated
solely in the language of categories, and no knowledge of type theory or
constructive set theory is required on the reader's part.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn