nLab
direct limit
Context
Category theory
category theory

Concepts
Universal constructions
Theorems
Extensions
Applications
Limits and colimits
limits and colimits

1-Categorical
limit and colimit

limits and colimits by example

commutativity of limits and colimits

small limit

filtered colimit

sifted colimit

connected limit , wide pullback

preserved limit , reflected limit , created limit

product , fiber product , base change , coproduct , pullback , pushout , cobase change , equalizer , coequalizer , join , meet , terminal object , initial object , direct product , direct sum

finite limit

Kan extension

weighted limit

end and coend

2-Categorical
(∞,1)-Categorical
Model-categorical
The term direct limit is essentially another term for colimit , dating from a time before category theoretic terminology became established. It is still used in various areas of mathematics. (Dually , inverse limit is another term for limit .) In this terminology, direct system means diagram , and direct cone means cocone .

More specifically, the term direct limit is often understood by default to refer to colimits over directed sets (or filtered categories ); see directed colimit (or filtered colimit ) for discussion of this case.

Especially common here is the directed set $(\mathbb{N},\leq)$ of natural numbers , in which case the direct system may be called a direct sequence .

Last revised on April 24, 2021 at 03:36:56.
See the history of this page for a list of all contributions to it.