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Colimits of categories, zig-zags and necklaces | | Redi Haderi
; | | Date: |
1 Sep 2023 | | Abstract: | Given a diagram of small categories $F : J
ightarrow extbf{Cat}$, we
provide a combinatorial description of its colimit in terms of the indexing
category $J$ and the categories and functors in the diagram $F$. We introduce
certain double categories of zig-zags in order to keep track of the necessary
identifications. We found these double categories necessary, but also
explanatory.
When applied pointwise in the simplicially enriched setting, our
constructions offer a shorter proof of the necklace theorem of Dugger and
Spivak by direct computation. | | Source: | arXiv, 2309.00337 | | Services: | Forum | Review | PDF | Favorites | |
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