strict initial object
Limits and colimits
limits and colimits
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
An initial object is called a strict initial object if any morphism must be an isomorphism.
The initial objects of a poset, of Set, Cat, Top, and of any topos (more generally of any extensive category) are strict.
At the other extreme, a zero object is only a strict initial object if the category is trivial (equivalent to the terminal category).