Displaying similar documents to “Lie groupoids of mappings taking values in a Lie groupoid”

Travel groupoids

Ladislav Nebeský (2006)

Czechoslovak Mathematical Journal

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In this paper, by a travel groupoid is meant an ordered pair ( V , * ) such that V is a nonempty set and * is a binary operation on V satisfying the following two conditions for all u , v ∈ V : ( u * v ) * u = u ; if ( u * v ) * v = u , then u = v . Let ( V , * ) be a travel groupoid. It is easy to show that if x , y ∈ V , then x * y = y if and only if y * x = x . We say that ( V , * ) is on a (finite or infinite) graph G if V ( G ) = V and E ( G ) = { { u , v } u , v ∈ V and u ≠ u * v = v } . Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.

Orbit projections of proper Lie groupoids as fibrations

Armin Rainer (2009)

Czechoslovak Mathematical Journal

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Let 𝒢 ⇉ M be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection M → M / 𝒢 is a fibration if and only if 𝒢 ⇉ M is regular.