Functor

Monoid

Group

Ring

A result that relates functors to natural transformations.

A theorem that characterizes the category of sets.

A statement about the existence of universal objects.

A principle that underlies the construction of free categories.

A category with a tensor product and a unit object.

A category with a product and a coproduct.

A category with a zero object and a terminal object.

A category with a group object and a group homomorphism.

Category theory provides a framework for understanding the mathematical structure of quantum mechanics.

Quantum mechanics can be formulated as a category theory.

Category theory is used to develop new quantum algorithms.

Category theory is used to study the foundations of quantum gravity.

A theory that describes the behavior of quantum fields on a topological space.

A theory that unifies general relativity and quantum mechanics.

A theory that explains the origin of dark matter.

A theory that predicts the existence of supersymmetry.

A duality between a conformal field theory and a string theory.

A duality between a gauge theory and a gravity theory.

A duality between a topological quantum field theory and a conformal field theory.

A duality between a quantum field theory and a statistical mechanics model.

A mathematical object that is used to describe the spin of a particle.

A mathematical object that is used to describe the polarization of a photon.

A mathematical object that is used to describe the geometry of spacetime.

A mathematical object that is used to describe the interaction of particles.

A diagram that is used to represent the geometry of spacetime.

A diagram that is used to represent the evolution of a quantum state.

A diagram that is used to represent the interaction of particles.

A diagram that is used to represent the topology of a manifold.

A type of radiation that is emitted by black holes.

A type of radiation that is emitted by neutron stars.

A type of radiation that is emitted by white dwarfs.

A type of radiation that is emitted by pulsars.

A paradox that arises from the combination of quantum mechanics and general relativity.

A paradox that arises from the combination of special relativity and quantum mechanics.

A paradox that arises from the combination of general relativity and classical mechanics.

A paradox that arises from the combination of quantum mechanics and classical mechanics.

A principle that states that the information in a region of spacetime can be encoded on a boundary of that region.

A principle that states that the information in a region of spacetime can be encoded on a surface within that region.

A principle that states that the information in a region of spacetime can be encoded on a point within that region.

A principle that states that the information in a region of spacetime can be encoded on a line within that region.

A theory that unifies all of the fundamental forces of nature.

A theory that unifies general relativity and quantum mechanics.

A theory that explains the origin of dark matter.

A theory that predicts the existence of supersymmetry.

A theory that describes the fundamental constituents of matter as tiny, vibrating strings.

A theory that describes the fundamental constituents of matter as point particles.

A theory that describes the fundamental constituents of matter as waves.

A theory that describes the fundamental constituents of matter as fields.

A theory that describes gravity as a network of loops.

A theory that describes gravity as a field.

A theory that describes gravity as a wave.

A theory that describes gravity as a particle.

A theory that describes gravity as a network of triangles.

A theory that describes gravity as a field.

A theory that describes gravity as a wave.

A theory that describes gravity as a particle.