A locally polypresentable category is similar to a locally presentable category, but where we ask only for the existence of wide pullbacks rather than all small limits.
(locally polypresentable category)
A category $\mathcal{C}$ is called locally polypresentable if
it is an accessible category;
it has all wide pullbacks.
The second condition is equivalent to:
2’. it has all small polycolimits?.
The definition is due to
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