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 $(\mathbb{N},\leq)$ 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.
See the history of this page for a list of all contributions to it.