In category theory, algebras and coalgebras are abstractions which are often used to reason mathematically about computation. Higher-order instances are now being investigated to deepen our understanding of a diverse set of computational themes such as dependent types, recursive programming schemes, higher-order syntax, etc. The first half of the work investigates a very particular instance of higher-order coalgebras constructed from stream coalgebras. Using this work as motivation, the dissertation proceeds to the complete characterization of initial and final objects in (higher-order) algebra and coalgebra categories which are constructed from parameterized endofunctors on lower-level categories. The result generalizes two results in the literature concerning (1) algebras in arrow categories and (2) coalgebras for iteratable endofunctors. The approach gives a unified view of what is happening in these results and gives a general framework for approaching similar but more specialized higher-order situations.
|Commitee:||Connell, Christopher, Haghverdi, Esfandiar, Leivant, Daniel|
|School Location:||United States -- Indiana|
|Source:||DAI-B 75/05(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical Mathematics|
|Keywords:||Coalgebras, Higher-order algebras, Parameterized endofunctors, Stream coalgebras|
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