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A Study of Categories of Algebras and Coalgebras

Summary: A Study of Categories of Algebras
and Coalgebras
Jesse Hughes
May, 2001
Department of Philosophy
Carnegie Mellon University
Pittsburgh PA 15213
Thesis Committee
Steve Awodey, Co-Chair
Dana Scott, Co-Chair
Jeremy Avigad
Lawrence Moss, Indiana University
Submitted in partial fulfillment of the requirements for the degree of Doctor of
This thesis is intended to help develop the theory of coalgebras by, first, taking
classic theorems in the theory of universal algebras and dualizing them and, second,
developing an internal logic for categories of coalgebras.
We begin with an introduction to the categorical approach to algebras and the
dual notion of coalgebras. Following this, we discuss (co)algebras for a (co)monad


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University
Hughes, Jesse - Department of Technology Management, Technische Universiteit Eindhoven


Collections: Computer Technologies and Information Sciences; Mathematics