Introduction
Category theory
as a purely formal tool
Category theory
based formulation of the ontology of TGD Universe
Other
applications
What categories
are?
Basic concepts
Presheaf as a
generalization of the notion of set
Generalized
logic defined by category
Category theory and
consciousness
The ontology of
TGD is tripartistic
The new ontology
of spacetime
The new notion
of subsystem and notions of quantum presheaf and quantum logic
Does quantum
jump allow spacetime description?
Brief
description of the basic categories related to the self
hierarchy
The category of
light cones, the construction of the configuration space
geometry, and the problem of psychological time
More precise
characterization of the basic categories and possible
applications
Intuitive
picture about the category formed by the geometric correlates
of selves
Categories
related to self and quantum jump
Communications
in TGD framework
Cognizing about
cognition
Logic and category
theory
Is the logic of
conscious experience based on set theoretic inclusion or
topological condensation?
Do configuration
space spinor fields define quantum logic and quantum topos?
Category theory
and the modelling of aesthetic and ethical judgements
Platonism, Constructivism, and
Quantum Platonism
Platonism and structuralism
Structuralism
The view about mathematics
inspired by TGD and TGD inspired theory of consciousness
Farey sequences, Riemann hypothesis, tangles, and TGD
Quantum Quandaries
The *category of Hilbert spaces
The monoidal *category of Hilbert spaces and its counterpart at the level of nCob
TQFT as a functor
The situation is in TGD framework
How to represent algebraic numbers as geometric objects?
Can one define complex numbers as cardinalities of sets?
In what sense a set can have cardinality 1?
Generalization of the notion of rig by replacing naturals with padic integers
Gerbes and TGD
What gerbes
roughly are?
How do 2gerbes
emerge in TGD?
How to
understand the replacement of 3cycles with ncycles?
Gerbes as
gradedcommutative algebra: can one express all gerbes as products of 1 and 0gerbes?
The physical
interpretation of 2gerbes in TGD framework
Appendix: Category theory and construction of
Smatrix
