The notion of a class-locally presentable category is a generalisation of that of a locally presentable category: In a class-locally presentable category one may need a proper class of objects (instead of just a small set) to build all the others by suitable colimits.
Let be a regular cardinal, and let the category be complete and cocomplete. Then is called class -presentable if there is a class of -presentable objects such that every object of is a -filtered colimit of objects in . A category is class-locally presentable if it is class -presentable for some .
If merely has -filtered colimits, rather than all colimits (and limits), then it is called class -accessible, and class-accessible if it is class -accessible for some .
216, Issue 10 (2012) pp 2113–2125 (doi:10.1016/j.jpaa.2012.01.015)
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