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[Hasegawa Masahito]

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$BD9C+ at n???M(B <hassei at kurims.kyoto-u.ac.jp>
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$B!V(BCategorical Algebra and Coalgebra:
  An Instance of Category Theory in Computer Science$B!W(B
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Abstract
Category theory is an abstract mathematical language that is used in
many different branches of mathematics. It has also found successful
applications in computer science - in fact, in many different
ways. The classic example is in the semantics of functional
programming, where types are objects and programs are arrows. In this
course we focus on another eminent use of categories in computer
science, namely categorical algebra and coalgebra. 
  The bottom-line here is: a coalgebra is a categorical abstraction of 
dynamics, i.e. a state-based system like an automaton; and an algebra
(especially an initial one) is an abstraction of syntax, i.e. the set
of well-formed programs. Plotkin's structural operational semantics -
connecting syntax and dynamics - also allows an elegant categorical
modeling via a distributive law. 
  After exhibiting these basics of the (co)algebraic modeling in
computer science, we proceed to a more advanced categorical structure
of presheaf categories. We introduce the necessary categorical
machineries - (co)end, Kan extension, Yoneda lemma, etc. - as well as 
demonstrate their applications in name-passing calculi like the
pi-calculus. 
  No preliminary knowledge in category theory is assumed. The course
materials will be announced at the course website.

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http://www.kurims.kyoto-u.ac.jp/~hassei/hasuo2012.pdf