lean2/hott/types/types.md

hott.types

Types in Martin-Lӧf Type Theory:

• unit
• bool
• [num[(num.hlean) (natural numbers written in binary form)
• nat (subfolder)
• int (subfolder)
• prod
• sigma
• sum
• pi
• arrow
• arrow_2: alternative development of properties of arrows
• W: W-types (not loaded by default)
• lift
• list

The number systems (num, nat, int, ...) are for a large part ported from the standard libary.

Specific HoTT types

• eq: show that functions related to the identity type are equivalences
• pointed: pointed types, pointed maps, pointed homotopies
• fiber
• equiv
• pointed2: pointed equivalences and pointed truncated types (this is a separate file, because it depends on types.equiv)
• trunc: truncation levels, n-types, truncation
• pullback
• univ