In mathematics, a **direct limit** (also called **inductive limit**) is a colimit of a "directed family of objects". We will first give the definition for algebraic structures like groups and modules, and then the general definition which can be used in any category.

Read more about Direct Limit: Examples, Related Constructions and Generalizations

### Other articles related to "direct limit, limit, limits, direct limits, direct":

**Direct Limit**- Related Constructions and Generalizations

... The categorical dual of the

**direct limit**is called the inverse

**limit**(or projective

**limit**) ... More general concepts are the

**limits**and colimits of category theory ... The terminology is somewhat confusing

**direct limits**are colimits while inverse

**limits**are

**limits**...

... that K0(A) is finitely generated and, since K0 respects

**direct limits**, K0(B) = ∪n βn* K0 (Bn) ... between dimension groups, one constructs a diagram of commuting triangles between the

**direct**systems of A and B by applying the second lemma ... Using the property of the

**direct limit**and moving A2 further down if necessary, we obtain diagram 4, a commutative triangle on the level of K0 ...

**Direct Limit**Of Groups

... In mathematics, a

**direct limit**of groups is the

**direct limit**of a

**direct**system of groups ... "unstable" groups, the groups occurring in the

**limit**... are generally infinite-dimensional, constructed as

**limits**of groups with finite-dimensional representations ...

... timeouts Plug

... two properties of Riesz groups are preserved by

**direct limits**, assuming the order structure on the

**direct limit**comes from those in the inductive system ... the fact that every Riesz group is the

**direct limit**of Zk 's, each with the canonical order structure ... Corollary Every Riesz group (G, G+) can be expressed as a

**direct limit**where all the connecting homomorphisms in the directed system on the right hand side are positive ...

### Famous quotes containing the words limit and/or direct:

“Berowne they call him, but a merrier man,

Within the *limit* of becoming mirth,

I never spent an hour’s talk withal.”

—William Shakespeare (1564–1616)

“One merit in Carlyle, let the subject be what it may, is the freedom of prospect he allows, the entire absence of cant and dogma. He removes many cartloads of rubbish, and leaves open a broad highway. His writings are all unfenced on the side of the future and the possible. Though he does but inadvertently *direct* our eyes to the open heavens, nevertheless he lets us wander broadly underneath, and shows them to us reflected in innumerable pools and lakes.”

—Henry David Thoreau (1817–1862)