Point axioms and related conditions in Dedekind categories

•The interrelations between several axioms related to point axioms have been shown.•We have explored the axiom of totality and the axiom of complement in detail.•We remark fundamental facts on L-relations related to the relational axiom of choice.

A Dedekind category is a convenient algebraic framework to manipulate (binary) relations. Concepts of points, point axioms and related conditions such as the axiom of totality, the axiom of subobject, the axiom of complement, and the relational axiom of choice are introduced in Dedekind categories in order to connect abstract notions to set-theoretical intuition. This paper summarises logical interrelations of these axioms and provides some ideas for using them.