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 it is a subobject of 1, hence the name.[2] The category of categories with subterminal objects and functors preserving them is not accessible.[3]

References
  1. Pitt, David; Rydeheard, David E.; Johnstone, Peter (12 September 1995). Category Theory and Computer Science: 6th International Conference, CTCS '95, Cambridge, United Kingdom, August 7 - 11, 1995. Proceedings. Springer. Retrieved 18 February 2017.
  2. Ong, Luke (10 March 2010). Foundations of Software Science and Computational Structures: 13th International Conference, FOSSACS 2010, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2010, Paphos, Cyprus, March 20-28, 2010, Proceedings. Springer. ISBN 9783642120329. Retrieved 18 February 2017.
  3. Barr, Michael; Wells, Charles (September 1992). "On the limitations of sketches". Canadian Mathematical Bulletin. Canadian Mathematical Society. 35 (3): 287–294. doi:10.4153/CMB-1992-040-7.
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