Subterminal object

In category theory, a branch of mathematics, a subterminal object is an object "X" of a category "C" with the property that every object of "C" has at most one morphism into "X". If "X" is subterminal, then the pair of identity morphisms (1"X", 1"X") makes "X" into the product of "X" and "X". If "C" has a terminal object 1, then an object "X" is subterminal if and only if it is a subobject of 1, hence the name. The category of categories with subterminal objects and functors preserving them is not accessible.