nLab
projective 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
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 $(\mathbb{N},\geq)$ 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 .

Revised on September 16, 2017 10:57:45
by

Tim Porter
(2a01:cb08:818d:3e00:25a2:125:2a4c:e351)