A full subcategory 
of a category 
is a subcategory such that,
for every pair of objects 
of 
,
 |
Thus a full subcategory contains every morphism in 
between the objects it contains.
Full Subcategory
See also
Category, Fully Faithful Functor, Object, SubcategoryExplore with Wolfram|Alpha
References
Mac Lane, S. Categories for the Working Mathematician. New York: Springer-Verlag, 1971. https://doi.org/10.1007/978-1-4612-9839-7.Cite this as:
Weisstein, Eric W. "Full Subcategory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FullSubcategory.html