Limit (category theory)

<p>In <a href="/facts/Category_theory/6zS3DXPa">category theory</a>, a branch of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the abstract notion of a limit captures the essential properties of universal constructions such as <a href="/facts/Product_(category_theory)/evFecz0t">products</a>, <a href="/facts/Pullback_(category_theory)/bC0QoX5U">pullbacks</a> and <a href="/facts/Inverse_limit/f6QecRUu">inverse limits</a>.  The <a href="/facts/Duality_(category_theory)/frtUrhBq">dual notion</a> of a colimit generalizes constructions such as <a href="/facts/Disjoint_union/x9QSfkr5">disjoint unions</a>, <a href="/facts/Direct_sum/x3ljVsP6">direct sums</a>, <a href="/facts/Coproduct/0bJ8SCdu">coproducts</a>, <a href="/facts/Pushout_(category_theory)/6wuns0Yo">pushouts</a> and <a href="/facts/Direct_limit/V3JuHnYK">direct limits</a>.
</p><p>Limits and colimits, like the strongly related notions of <a href="/facts/Universal_property/5XJBYMNz">universal properties</a> and <a href="/facts/Adjoint_functors/bJ1P7AN2">adjoint functors</a>, exist at a high level of abstraction. In order to understand them, it is helpful to first study the specific examples these concepts are meant to generalize.
</p>

Limit (category theory) open-in-new

Limit (category theory)