This text scrutinises the genesis of the concept of intersectionality, coined by Kimberlé Crenshaw in 1991, highlighting the social, theoretical and institutional conditions of its invention, which is not unrelated to the author's dual belonging as an academic (jurist) and African American activist for black women's rights. Two types of intersectionality are then presented: one, avantla lettre, more abstract and general (type 1), of a systemic and structural nature, which includes the societal theories of Pierre Bourdieu and Karl Marx. Another, closer to the phenomenological ground of experience type 2), whose starting point is drawn up precisely by Crenshaw.The concept is subjected to a holistic and materialist critique, associated with Nancy Fraser's idea of capitalism as an institutionalised social order, highlighting the potential of intersectionality, particularly in the updates that Crenshaw has incorporated, but also the theoretical and civic risks of atomisation, differentialism and individualistic identity appropriation. Finally, it is suggested that type 1 and type 2 of intersectionality should be crossed.