Exact categories of coalgebras
DOI:
https://doi.org/10.17398/Keywords:
Barr-exact category, coalgebra, effective equivalence relation, factorization system, pullbackAbstract
Let F : C → C be an endofunctor and, write CF the category of F -coalgebras. The endofunctor F is called a covarietor when the forgetful functor U : CF → C has a right adjoint. Assuming C is Barr-exact (i.e., regular and internal equivalence relations are effective), we prove that CF is Barr-exact under the condition F is a covarietor and preserves pullbacks.
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