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 (1X, 1X) 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


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