nLab
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
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 .
Many authors restrict this terminology to colimits over directed sets (or filtered categories ), especially the directed set ( ℕ , ≤ ) natural numbers ; see directed colimit (or filtered colimit ) for discussion of this case if you think that it may be what you want.
Revised on July 28, 2011 02:00:58
by
Toby Bartels
(76.85.192.183)