We show that the category of coalgebras of a wide-pullback preserving endofunctor on a category of presheaves is itself a category of presheaves. This illustrates a connection between Jacobs' temporal logic of coalgebras and Ghilardi and Meloni's presheaf semantics for modal logic. © 2002 Published by Elsevier Science B.V.
Worrell, J. (2005). A note on coalgebras and presheaves. In Mathematical Structures in Computer Science (Vol. 15, pp. 475–483). https://doi.org/10.1017/S0960129505004767