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<p> together with the canonical homomorphisms .</p>

<p><big> Direct limits in an arbitrary category </big></p>
<p>The direct limit can be defined in an arbitrary <a href="page.php?w=category_%28mathematics%29">category</a>  by means of a <a href="page.php?w=universal_property">universal property</a>. Let  be a direct system of objects and morphisms in  (as defined above). A target is a pair  where  is an object in  and  are morphisms for each  such that  whenever  . A direct limit of the direct system  is a universally repelling target  in the sense that</p><p>
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