Homotopy colimits in the vertical simplicially enriched category of a higher equipment coincide with double colimits of companion diagrams, unifying double category theory with homotopy theory.
Span and cospan representations of weak double categories
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Higher Equipments, Double Colimits and Homotopy Colimits
Homotopy colimits in the vertical simplicially enriched category of a higher equipment coincide with double colimits of companion diagrams, unifying double category theory with homotopy theory.