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.{{cite book|url=https://books.google.com/books?id=GJRQAAAAMAAJ|title=Category Theory and Computer Science: 6th International Conference, CTCS '95, Cambridge, United Kingdom, August 7 - 11, 1995. Proceedings|first=David|last=Pitt|first2=David E.|last2=Rydeheard|first3=Peter|last3=Johnstone|date=12 September 1995|publisher=Springer|access-date=18 February 2017}} 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.{{cite book|url=https://books.google.com/books?id=HCiqCAAAQBAJ|title=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|first=Luke|last=Ong|date=10 March 2010|publisher=Springer|isbn=9783642120329|access-date=18 February 2017}} The category of categories with subterminal objects and functors preserving them is not accessible.{{cite journal|first=Michael|last=Barr|first2=Charles|last2=Wells|date=September 1992|title=On the limitations of sketches|magazine=Canadian Mathematical Bulletin|volume=35|issue=3|pages=287–294|publisher=Canadian Mathematical Society|doi=10.4153/CMB-1992-040-7|doi-access=free}}