Homotopy Type Theory Algebra > history (Rev #35)

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?

Rings

• abelian group
• divisible group
• torsion-free divisible group
• halving group
• abelian group homomorphism
• bilinear function
• ring
• commutative ring
• univariate polynomial ring

Sequences

• sequence
• left shift operator
• right shift operator
• Z-module
• sequential polynomial
• series operator
• inverse series operator
• sequential derivative
• Q-vector space
• sequential antiderivative

References

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