
This paper gives a tour of join constructions for topological spaces, simplicial sets and small categories, with evident comparisons. The unifying theme is that the join of two objects \(X\) and \(Y\) is the homotopy colimit of the diagram of projections \(X \leftarrow X \times Y \to Y\).
mapping cylinders, Homotopy functors in algebraic topology, Simplicial sets; simplicial objects in a category, joins, Abstract and axiomatic homotopy theory in algebraic topology
mapping cylinders, Homotopy functors in algebraic topology, Simplicial sets; simplicial objects in a category, joins, Abstract and axiomatic homotopy theory in algebraic topology
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