Internal Reflexive Relation

An internal reflexive relation is a Jointly Monic Pair X ← p 1 R → p 2 X subscript 𝑝 1 ← 𝑋 𝑅 subscript 𝑝 2 → 𝑋 X\xleftarrow{p_{1}}R\xrightarrow{p_{2}}X along with a Morphism of Spans r 𝑟 r

X𝑋{X}X𝑋{X}X𝑋{X}R𝑅{R}mathrmidifx..⋄lsei\scriptstyle{mathrm{id}{ifx..lse\par i}}mathrmidifx..⋄lsei\scriptstyle{mathrm{id}{ifx..lse\par i}}r𝑟\scriptstyle{r}p1subscript𝑝1\scriptstyle{p_{1}}p2subscript𝑝2\scriptstyle{p_{2}}

from the identity span.