category

1. what is category?

In a category, there are a set of objects, a set of arrows to build relationship between objects. They keep identity and associative rules.

plan for this week (11.23 – 12.03)

Today is Wednesday, and half of the week. It seems I have not do something It is very bad for me in this situation.

Last week I read some stuff in category theory:

(1) Category theory for beginners, given by the CS department, University of Toronto. It describes basic definition of category, important concepts (functor, initial and terminal, colimit and limit, etc), and why we need category in CS. Now I have a sketcial impression. Category describes the objects and relationship between them. It puts emphasis on the relationship, and it even does not care about the structure of the objects. It seems close to the thought of object-oriented methodology. It is useful in abstraction, reasoning, and automation. Because it can provide formal means for composition and decompositon, it can have good application in SE.

(2) A tutorial on (co)algebra and (co)induction, given by Bart Jacobs. It is very good because it gives some examples for each situation. But I can not get too much, because I lack the necessary background in category theory. It is hard to read.

(3) Recursive Domain Equations, given by Mads Sig Ager, 2002. It is too abstract.

(4) finite data structures? given by Henning Korshlom Rohde, 2002. Apply category theory to construct data structure.

(5) A categorical manifesto, given by Joseph A.Goguen, university of Cambridge. It gives seven guidelines for application of category by demonstrating its features deeply.

At the beginning of this week, I read Simon’ reports, and hope to find the ways that category theory applies to contextual information.

(1) Semantics in pervasive computing, a talk given in Trinity, 2003.

(2) Motivating a model of computation for pervasive computing. He regards the context and behavior as two categories, and constructs functor between them. By fiber, he can ,,,, The concepts he uses are fiber, functor, composition of categories, coalgebra.

(3) A model of computation for context-aware systems, 2003. He details the thought and means to apply category in contextual information by a concrete example. And he gives some problems left open to solve.

(4) Some motivations and possible approaches to a semantics of adaptive systems.

The left of this week and next week, I hope to finish a book “Category theory”, CMU. And hopefully, I can associate the concepts with pervasive computing. So the plan is written as following:

1. morning: a paper for application;

2. afternoon & evening: book

past work

At first, I mainly read some papers about modeling contextual information in pervasive computing. Popular ways are ontology and RDF. I read a serial of papers writen by Henricken, and T.Strang.

Then I read some stuff about ontology, and current reasoning techniques, such as SWRL, description logic, etc.