Homotopy Type Theory fully faithful > history (Rev #2, changes)

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I (Victor Porton) have the following (very preliminary) idea:

Idea

Replace “path” in the definition of homotopy with “monovalued funcoid with domain [0;1]”. It enables things like infinitely short paths. This way we may get another HoTT possibly not equivalent to the “main” HoTT.

Definition

This A idea uses theory functor of funcoids (discovered by me).F:ABF : A \to B is faithful if for all a,b:Aa,b : A, the function

F a,b:hom A(a,b)hom B(Fa,Fb)F_{a,b} : hom_A(a,b) \to hom_B(F a, F b)

is injective?, and full if for all a,b:Aa,b : A this function is surjective?. If it is both then FF is fully faithful

See also

Category theory functor equivalence of precategories

References

HoTT Book

category: category theory

Revision on September 14, 2018 at 12:00:07 by Ali Caglayan. See the history of this page for a list of all contributions to it.