Sets are fundamental to modern mathematics, but the most general conception of set proved to be incoherent and was quickly
replaced (for most mathematical work) by the narower, coherent, conception of sets which arises from the constraint of well-foundedness.

This constraint is however pragmatically onerous, and research has continued on broader conceptions of set.
One particular source of motivation for non well-founded sets can be found in the pragmatics of practical formalisation of
mathematics, and it is this domain which guides the work I am engaged in on infinitary comprehension.