category theory Concepts
Limits and colimits
limits and colimits 1-Categorical
limit and colimit
limits and colimits by example
commutativity of limits and colimits
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
end and coend 2-Categorical
direct limit is the same thing as a colimit, which was often used before the categorical terminology started to become ‘standardised’. It is still used in certain areas of mathematics. (Similarly, an inverse limit is the same thing as a limit.) In this context, a direct system is the same thing as a diagram, and a direct cone is the same thing as a cocone.
Many authors restrict this terminology to limits over
directed sets (or filtered categories); see (or directed colimit ) for discussion of this case if you think that it may be what you want, or see filtered colimit for the more general notion. Especially common is the directed set colimit of ( ℕ , ≤ ) natural numbers, in which case the direct system may be called a direct sequence.
Revised on April 27, 2012 16:03:00