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48 Chapter 4. Mal’tsev aspects of Mon upper row becomes an equivalence relation, and, moreover, the two commuta-
tive squares in the diagram below are pullbacks:
R× Soo p1 //S
// OO dR1 //
OOX
(dR0 p0,p) dS0
p0
When R and S are equivalence relations, all the reflexive relations in this di- agram are equivalence relations, and, moreover, the four commutative squares in diagram 4.4.1 are pullbacks.
When G is a group and (R,S) is a pair of equivalence relations on G centralizing each other, the square of related elements is the following one:
x S //z·y−1·x R // R
y z.
S
When M is a monoid and (R, S) is a pair of reflexive relations on M centralizing each other, with S a Schreier one, we noticed that the square of related elements is the following one:
x S // q(ySz)·x R // R
y z.
S
R oo
// X
dR0
