The Righteous Mind (2012).
There are five core moral foundations in Moral Foundations Theory.
2 Equality-Fairness; aka fairness/cheating*
4 Authority-Respect; aka Authority/subversion
5 Purity-Sanctity aka Sanctity/degradation
An additional foundation of liberty has been added to the theory so there are now six foundations.
Researchers usually find support for a two factor model. Conservatives view moral issues from 3-5 perspectives with an emphasis on the foundations of loyalty, authority, and purity. Sociopolitical liberals emphasize care and fairness foundations. In A House Divided, I consider examples of Christians using the same foundations in different ways. For example, in abortion arguments conservatives focus on care and harm of the unborn child and liberals emphasize care-harm concerns of the mother.
*I added the "aka" because you will find somewhat different words in some articles.
See this page for a description of the five core foundations https://www.moralfoundations.org/
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Here are some applications of moral foundations theory:
For applications to Christian views of moral issues see A House Divided: Sexuality, Morality and Christian Cultures.
For a recent study of Moral Foundations Theory, Identity, and Politics, see Sutton, Kelly, and Huber (2019).
Link to learn more about the Moral Foundations Questionnaire