An axiomatics for categories of coalgebras

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• 作者：John Power ; Hiroshi Watanabe
• 刊名：Electronic Notes in Theoretical Computer Science
• 出版年：1998
• 出版时间：1998
• 年：1998
• 卷：11
• 期：Complete
• 页码：158-175
• 全文大小：841 K

文摘

We give an axiomatic account of what structure on a category C and an endofunctor H on C yield similar structure on the category H —Coalg of H-coalgebras. We give conditions under which completeness, cocompleteness, symmetric monoidal closed structure, local presentability, and subobject classifiers lift. Our proof of the latter uses a general result about the existance of a subobject classifier in a category containing a small dense subcategory. Our leading example has C = Set with H the endofunctor for which a coalgebra is a finitely branching (labelled) transition system. We explain that example in detail.