For questions about locally presentable categories.

A locally small cocomplete category $\mathcal{C}$ is called locally presentable if there exists a regular cardinal $\lambda$ such that $\mathcal{C}$ is generated under $\lambda$-filtered colimits by a set of $\lambda$-small objects.

These categories can be characterized as the categories of models of limit sketches.

See also the nLab, Wikipedia.

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