  We generalize the notion of an admissible ideal from path algebras to (small)
k-linear categories that satisfy the Krull--Remak--Schmidt--Azumaya assumption.
In our treatment we first prove some general results that are analogous to
general results for path algebras and admissible ideals. We then cover
generalizations of relations generated by paths of length two, which we call
point relations, and more general length relations. We conclude the paper with
several examples and an appendix containing further discussion on length
relations.
