# Notes: "Seven Sketches in Compositionality"

transitive: a `op`

b AND b `op`

c => a `op`

c (relation is contagious)

a ~ b :: a and b in same ("equivalence relation") partition

reflextivity: $c ~ c$

symmetry: a ~ b iff b ~ a

transitive: a ~ b and b ~ c => a ~ c

function: from S to T where (s,t) subset of S x T, t = F(s) i.e. all source objects have a target object

surjective function: For all t there exists and t = F(s) i.e. all targets in T are reachable from S (S ->> T)

injective function: For all t and t = F(s1) = F(s2) then s1 = s2 i.e. all target objects have a unique source object (S >-> T)

composite function: G(F(x)) : G . F "G after F" : F.G "F then G"

preorder relation in set X where:

- reflextivity: x <= x
- transitive: a ~ b and b ~ c => a ~ c

equivalence: if a <= b and b <= a then a ≃ b