More results from the Spectral repository are moved to this library
Also make various type-class arguments of truncatedness and equivalences which were hard to synthesize explicit
some of the changes are backported from the hott3 library
pi_pathover and pi_pathover' are interchanged (same for variants and for sigma)
various definitions received explicit arguments: pinverse and eq_equiv_homotopy and ***.sigma_char
eq_of_fn_eq_fn is renamed to inj
in definitions about higher loop spaces and homotopy groups, the natural number arguments are now consistently before the type arguments
All HITs which automatically have a point are pointed without a 'p' in front. HITs which do not automatically have a point do still have a p (e.g. pushout/ppushout).
There were a lot of annoyances with spheres being indexed by N_{-1} with almost no extra generality. We now index the spheres by nat, making sphere 0 = pbool.
This commit adds truncated 2-quotients, groupoid quotients, Eilenberg MacLane spaces, chain complexes, the long exact sequence of homotopy groups, the Freudenthal Suspension Theorem, Whitehead's principle, and the computation of homotopy groups of almost all spheres which are known in HoTT.
other changes:
- move result about connectedness of susp to homotopy.susp
- improved definition of circle multiplication
- improved the interface to join
more about pointed truncated types, including pointed sets.
also increase the priority of some basic instances that nat/num/pos_num/trunc_index have 0, 1 and + (in both libraries)
also move the notation + for sum into the namespace sum, to (sometimes) avoid overloading with add
