1. Research Focus: Badiou, Category Theory and Integrated Studies
AU MAIS graduate - interdisciplinary focus
Reader of Alain Badiou - living French philosopher
Logics of Worlds
With this work Badiou deploys Category Theory to develop a phenomenological account of the appearing of entities within a given world as a network of relations.
- interdisciplinary background

2. Category Theory Background
Developed from attempts to solve problems at the intersection of algebra and geometry.
Framework for all of mathematical theory
Category Theory itself has been used to study the relations between branches of mathematics and to help solve problems across branches.
Category Theory’s power comes from it’s ability to map and preserve abstract structures between domains.
- interdisciplinary background

3. Proposal for Integrated Studies
Category Theory: a tool for interdisciplinary research
Model how it operates between branches in mathematics for doing research between disciplines
Category Theory provides the argument for the autonomous discipline of interdisciplinary research.
It would be deployed as a method to clarify underlying abstract structures within disciplines and for mapping the relation of these structures between disciplines leading to the discovery of new disciplines beyond just hybridized disciplines.
Worlds = Categories = Disciplines

4. Diagrammatic Orientation
Diagrams play integral role
- interdisciplinary background

5. Basic Category Theory Operators
Object represented by a dot
Relation represented with an arrow
Combined you have a directed arrow between two objects
The arrow can be conceptualized as a morphism, relation, affect, action, touches, or sees.
- interdisciplinary background

6. Requirements for a category
Require an identity arrow to each object.
Composition of arrows to commute.
Associativity maintained in composition:
i º ( g º f ) = (i º g) º f
Minimal operators and requirements results in maximal expressive power at the level of abstraction.
- interdisciplinary background

7. Usage 1: Internal to discipline (category)
Relations within a category can be mapped
Structure formations within a category can be identified, e.g. limit

8. Plato’s Four Virtues of State
Chapter four of Plato’s Republic identifies four virtues of state with justice being the highest virtue:

9. Usage 2: Socrates Relates State to Individual
“Let the discovery which we made be now applied to the individual - if they agree, we shall be satisfied”
State Individual
Functors

10. Usage 3: Categories of Functors - Emergence of IS
State Individual

11. Summary Category Theory: a tool for interdisciplinary research
Model behaviour inside a discipline
Model behaviour between disciplines
Model new discoveries in the relational space between disciplines.

12. Challenges Category Theory is still rigorous
We still have the problem of initially mapping a discipline’s objects and relations.
- interdisciplinary background

13. Further Reading Diagrammatic Immanence, Rocco Gangle
Mathematics of the Transcendental, Alain Badiou
- interdisciplinary background