- fundamentals of set theory
- material set theory
- presentations of set theory
- structuralism in set theory
- class-set theory
- constructive set theory
- algebraic set theory

Given sets $A$ and $B$, the **injection set** $\mathrm{Inj}(A, B)$ is the set of injection between the set $A$ and $B$. In the foundations of mathematics, the existence of such a set may be taken to follow from the existence of power sets, from the axiom of subset collection, from the existence of function sets, or as an axiom (the **axiom of injection sets**) in its own right.

If the set theory has function sets, then the injection set between $A$ and $B$ is a subset of the function set between $A$ and $B$: $\mathrm{Inj}(A, B) \subseteq B^A$.

The universal property of the bijection set states that given a function $X \to \mathrm{Inj}(A, B)$ from a set $X$ to the injection set between sets $A$ and $B$, there exists a injection $A \times X \hookrightarrow B \times X$ in the slice category $\mathrm{Set}/X$.

Last revised on January 13, 2023 at 05:50:24. See the history of this page for a list of all contributions to it.