nLab
Morita morphism

Context

\infty-Lie theory

∞-Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

The most useful notion of homomorphism between Lie groupoids is not that of a functor internal to the category SmoothMfd of smooth manifolds (even though Lie groupoids can be regarded as internal groupoids in SmoothMfd), but is that of a morphism of smooth stacks (differentiable stacks) on the site SmoothMfd. To amplify this distinction in the literature a wealth of names and terms for these non-naïve homomorphisms is used, such as Morita morphism . In particular a Morita morphism which is a homotopy equivalence is a Morita equivalence.

Ways to present the correct notion of homomorphism include

Revised on March 2, 2014 11:38:53 by Coward Anonymous? (93.147.79.110)