category-theory-presentation/categories/20_What/210_Categorical_Properties.html
2013-02-28 16:49:12 +01:00

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<h2 class="base1">Categorical Properties</h2>
<p class="base1">Any property which can be expressed in term of category, objects, morphism and composition.</p>
<ul><li> <em class="yellow">Dual</em>: \(\D\) is \(\C\) with reversed morphisms.
</li><li> <em class="yellow">Initial</em>: \(Z\in\ob{\C}\) s.t. \(∀Y∈\ob{\C}, \#\hom{Z,Y}=1\)
<br/> Unique ("up to isormophism")
</li><li> <em class="yellow">Terminal</em>: \(T\in\ob{\C}\) s.t. \(T\) is initial in the dual of \(\C\)
</li><li> <em class="yellow">Functor</em>: structure preserving mapping between categories
</li><li> ...
</li></ul>