Morphism of Spans

A morphism f : R S : 𝑓 𝑅 𝑆 f:{{R}\to{S}} is a morphism of spans ( A R B ) ( A S B ) 𝐴 𝑅 𝐵 𝐴 𝑆 𝐵 (A\leftarrow R\to B)\Rightarrow(A\leftarrow S\to B) the following diagram commutes:

R𝑅{R}A𝐴{A}B𝐵{B}S𝑆{S}r1subscript𝑟1\scriptstyle{r_{1}}r2subscript𝑟2\scriptstyle{r_{2}}f𝑓\scriptstyle{f}s2subscript𝑠2\scriptstyle{s_{2}}s1subscript𝑠1\scriptstyle{s_{1}}

We can also consider a "non-vertical" notion of span morphism, which allows replaces the two triangles with squares.