1. Introduction

    1. Category theory as a purely formal tool

    2. Category theory based formulation of the ontology of TGD Universe

    3. Other applications

  2. What categories are?

    1. Basic concepts

    2. Presheaf as a generalization of the notion of set

    3. Generalized logic defined by category

  3. Category theory and consciousness

    1. The ontology of TGD is tripartistic

    2. The new ontology of space-time

    3. The new notion of sub-system and notions of quantum presheaf and quantum logic

    4. Does quantum jump allow space-time description?

    5. Brief description of the basic categories related to the self hierarchy

    6. The category of light cones, the construction of the configuration space geometry, and the problem of psychological time

  4. More precise characterization of the basic categories and possible applications

    1. Intuitive picture about the category formed by the geometric correlates of selves

    2. Categories related to self and quantum jump

    3. Communications in TGD framework

    4. Cognizing about cognition

  5. Logic and category theory

    1. Is the logic of conscious experience based on set theoretic inclusion or topological condensation?

    2. Do configuration space spinor fields define quantum logic and quantum topos?

    3. Category theory and the modelling of aesthetic and ethical judgements

  6. Platonism, Constructivism, and Quantum Platonism

    1. Platonism and structuralism

    2. Structuralism

    3. The view about mathematics inspired by TGD and TGD inspired theory of consciousness

    4. Farey sequences, Riemann hypothesis, tangles, and TGD

  7. Quantum Quandaries

    1. The *-category of Hilbert spaces

    2. The monoidal *-category of Hilbert spaces and its counterpart at the level of nCob

    3. TQFT as a functor

    4. The situation is in TGD framework

  8. How to represent algebraic numbers as geometric objects?

    1. Can one define complex numbers as cardinalities of sets?

    2. In what sense a set can have cardinality -1?

    3. Generalization of the notion of rig by replacing naturals with p-adic integers

  9. Gerbes and TGD

    1. What gerbes roughly are?

    2. How do 2-gerbes emerge in TGD?

    3. How to understand the replacement of 3-cycles with n-cycles?

    4. Gerbes as graded-commutative algebra: can one express all gerbes as products of -1- and 0-gerbes?

    5. The physical interpretation of 2-gerbes in TGD framework

  10. Appendix: Category theory and construction of S-matrix