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Constructive homotopy theory of marked semisimplicial sets. (arXiv:1809.11168v1 [math.CT])
来源于:arXiv
We develop the homotopy theory of semisimplicial sets constructively and
without reference to point-set topology to obtain a constructive model for
$\omega$-groupoids. Most of the development is folklore, but for a few results
the author is unaware of previously known constructive proofs. These include
the statements that the unit of the free simplicial set adjunction is valued in
weak equivalences and that the geometric product and cartesian product of
fibrant semisimplicial sets are weakly equivalent.
We then extend the development to marked semisimplicial sets in order to
obtain a constructive model for $(\omega, 1)$-categories. 查看全文>>