nLab weak Kan complex

Idea

A weak Kan complex [Boardman & Vogt (1973)] is a simplicial set for which all inner horns have a filler.

The notion was later popularized under the name quasi-category. See there for more.

References

• Michael Boardman, Rainer Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics 347 Springer (1973) [doi:10.1007/BFb0068547]