nLab
projective 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, a projective limit is the same thing as a limit . (Similarly, an inductive limit is the same thing as a colimit .) In this context, a projective system is the same thing as a diagram , and a projective cone is the same thing as a cone .
However, many authors restrict this terminology to limits over codirected sets (or cofiltered categories ), especially the codirected set ( ℕ , ≥ ) (\mathbb{N},\geq) of natural numbers ; see codirected limit (or cofiltered limit ) for discussion of this case if you think that it may be what you want.
The dual concept is inductive limit .
Last revised on September 16, 2017 at 14:57:45.
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