Restriction categories were introduced as a way of generalising the notion of partial map category. In this paper, we define a notion of cocompleteness for restriction categories, and describe the free cocompletion of a small restriction category as a suitably defined category of restriction presheaves. We also consider free cocompletions in the case where our restriction category is only locally small.
Keywords: restriction categories, cocompletion, presheaves, locally small
2020 MSC: 18B10, 18A35
Theory and Applications of Categories, Vol. 35, 2020, No. 22, pp 809-844.