# 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*.^{[1]} 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 the unique morphism from *X* to 1 is a monomorphism, hence the name. The category of categories with subterminal objects and functors preserving them is not accessible.^{[2]}

## See also

## References

- ↑ Subterminal object in
*nLab* - ↑ "On the limitations of sketches".
*Canadian Mathematical Bulletin*. Vol. 35 no. 3. Canadian Mathematical Society. September 1992.

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