Subterminal Object

A subterminal object in a category is an object such that, for every object , there is at most one morphism . If has a terminal object , then is subterminal iff the unique morphism is a monomorphism. Thus subterminal objects correspond to subobjects of the terminal object. In a topos, the subterminal objects form a Heyting algebra.

See also

Category, Monomorphism, Subobject, Terminal Object, Topos

Explore with Wolfram|Alpha

More things to try:

References

Mac Lane, S. and Moerdijk, I. Sheaves in Geometry and Logic: A First Introduction to Topos Theory. New York: Springer, 1994.

Cite this as:

Weisstein, Eric W. "Subterminal Object." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SubterminalObject.html

Subject classifications