#
nLab

function complex

### Context

#### Mapping spaces

**internal hom/mapping space**

### General abstract

### Topology

### Simplicial homotopy theory

### Differential topology

### Stable homotopy theory

### Geometric homotopy theory

In categories like sSet, the internal hom $[X,Y]$ between two objects is often called the *function complex* (“simplicial complex of functions from $X$ to $Y$).