Editing Isomorphism theorems (section)

=== Theorem D (universal algebra) ===
Let <math>A</math> be an algebra and denote <math>\operatorname{Con}A</math> the set of all congruences on <math>A</math>. The set
<math>\operatorname{Con}A</math> is a [[complete lattice]] ordered by inclusion.<ref>Burris and Sankappanavar (2012), p. 37</ref>
If <math>\Phi\in\operatorname{Con}A</math> is a congruence and we denote by <math>\left[\Phi,A\times A\right]\subseteq\operatorname{Con}A</math> the set of all congruences that contain <math>\Phi</math> (i.e. <math>\left[\Phi,A\times A\right]</math> is a principal [[filter (mathematics)|filter]] in <math>\operatorname{Con}A</math>, moreover it is a sublattice), then
the map  <math>\alpha:\left[\Phi,A\times A\right]\to\operatorname{Con}(A/\Phi),\Psi\mapsto\Psi/\Phi</math> is a lattice isomorphism.<ref>Burris and Sankappanavar (2012), p. 49</ref><ref>{{cite web |first1=William |last1=Sun |title=Is there a general form of the correspondence theorem? |url=https://math.stackexchange.com/q/2850331 |website=Mathematics StackExchange |access-date=20 July 2019}}</ref>