Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
identity type, equivalence of types, definitional isomorphism
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
For a quasi-category, a morphism in (an edge in the underlying simplicial set) is an equivalence if its image in the homotopy category is an isomorphism.
Equivalently, is an equivalence if it is the image of a functor of quasi-categories (i.e. a map of simplicial sets) out of the nerve , where is the interval groupoid. This is a quasi-categorical version of the general theorem-schema in higher category theory that any equivalence can be improved to an adjoint equivalence.
Last revised on August 5, 2020 at 16:38:11. See the history of this page for a list of all contributions to it.