In
category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
, 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
In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms a ...
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 In category theory, a branch of mathematics, a subobject is, roughly speaking, an object that sits inside another object in the same category. The notion is a generalization of concepts such as subsets from set theory, subgroups from group theory,M ...
of 1, hence the name. The category of categories with subterminal objects and functors preserving them is not
accessible
Accessibility is the design of products, devices, services, vehicles, or environments so as to be usable by people with disabilities. The concept of accessible design and practice of accessible development ensures both "direct access" (i.e ...
.
References
External links
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Category theory
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