nLab
inductive limit
Contents
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
fibered limit
2-Categorical
(∞,1)-Categorical
Model-categorical
Contents
Idea
Generally, an inductive limit is the same thing as a colimit . (Similarly, a projective limit is the same thing as a limit .) In this context, an inductive system is the same thing as a diagram , and an inductive cone is the same thing as a cocone .
However, many authors restrict this terminology to colimits over directed sets (or filtered categories ), especially the directed set ( ℕ , ≤ ) (\mathbb{N},\leq) of natural numbers ; see directed colimit (or filtered colimit ) for discussion of this case if you think that it may be what you want.
The dual concept is that of a projective limit .
Last revised on August 18, 2022 at 20:08:10.
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