Homotopy Type Theory Algebra > history (Rev #13)

Here we collect articles about doing set-level algebra in HoTT.

Decidable objects

• booleans
• decidable universal quantifier
• decidable existential quantifier
• decidable directed graph
• decidable setoid
• decidable set
• decidable preordered type
• decidable strict order
• decidable dense strict order?

Inverse images

• inverse image
• iterated inverse image
• infinitely iterated inverse image

Monoids

• monoid
• commutative monoid
• group
• abelian group/Z-module
• divisible group
• halving group/D-module
• torsion-free divisible group/Q-module
• action
• abelian group homomorphism
• bilinear function

Rings, modules, and algebras

• Z-module/abelian group
• Q-module/torsion-free divisible group
• abelian group homomorphism
• bilinear function
• ring
• commutative ring
• algebra (ring theory)
• Q-algebra
• commutative algebra (ring theory)
• polynomial ring
• univariate polynomial ring
• function algebra
• module
• graded module
• filtered algebra
• quadratic form
• Clifford algebra
• geometric algebra

Sequences

• sequence

• left shift operator

• right shift operator

• Z-module

• sequential polynomial

• series operator

• inverse series operator

• sequential derivative

• Q-module

• sequential antiderivative

• sequential differential operator?

• sequential linear differential equation?

• sequential exponential?

• sequential sine?

• sequential cosine?

• bidirectional sequence

• bidirectional shift operators?

Ordered commutative rings

• ordered integral domain
• Archimedean ordered integral domain
• ordered field
• Archimedean ordered field
• sequentially Cauchy complete Archimedean ordered field

References

• HoTT Book
• Henri Lombardi, Claude Quitté, Commutative algebra: Constructive methods. Finite projective modules, arXiv:1605.04832