equivalences in/of -categories
For a morphism in an (infinity,1)-category is an -monomorphism equivalently if
in its n-image factorization
the first morphism is an equivalence in an (infinity,1)-category
it is an (n-2)-truncated morphism;
Similarly a function in homotopy type theory is an -monomorphism if its -image factorization is via an equivalence in homotopy type theory.
The dual concept is that of n-epimorphism.
-monomorphism are precisely the equivalences.
Every morphism is an -monomorphism.
1-monomorphisms are often just called monomorphisms in an (∞,1)-category. The 1-monomorphisms into a fixed object are called the subobjects of that object.
A 1-monomorphism between 0-truncated objects is precisely an ordinary monomorphism in the underlying 1-topos.
Last revised on October 28, 2016 at 18:00:13. See the history of this page for a list of all contributions to it.