adjoint functor theorem
adjoint lifting theorem
small object argument
Freyd-Mitchell embedding theorem
relation between type theory and category theory
sheaf and topos theory
enriched category theory
higher category theory
Edit this sidebar
nice topological space
nice category of spaces
convenient category of topological spaces
Freudenthal suspension theorem
CW-complex, Hausdorff space, second-countable space, sober space
compact space, paracompact space
connected space, locally connected space, contractible space, locally contractible space
topological vector space, Banach space, Hilbert space
point, real line, plane
sphere, ball, annulus
loop space, path space
Cantor space, Sierpinski space
long line, Warsaw circle
A topological groupoid is an internal groupoid in the category Top.
So this is a groupoid with a topological space of objects and one of morphisms, and all structure maps (source, target, identity, composition) are continuous maps.
A topological groupoid C is called an open topological groupoid is the source map s:MorC→ObjC is an open map.
It is called an étale groupoid if in addition s is a local homeomorphism.