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- Title
Functors (between ∞-categories) that aren’t strictly unital.
- Authors
Tanaka, Hiro Lee
- Abstract
Let C<inline-graphic></inline-graphic> and D<inline-graphic></inline-graphic> be quasi-categories (a.k.a. ∞<inline-graphic></inline-graphic>-categories). Suppose also that one has an assignment sending commutative diagrams of C<inline-graphic></inline-graphic> to commutative diagrams of D<inline-graphic></inline-graphic> which respects face maps, but not necessarily degeneracy maps. (This is akin to having an assignment which respects all compositions, but may not send identity morphisms to identity morphisms.) When does this assignment give rise to an actual functor? We show that if the original assignment can be shown to respect identity morphisms up to homotopy, then there exists an honest functor of ∞<inline-graphic></inline-graphic>-categories which respects the original assignments up to homotopy. Moreover, we prove that such honest functors can be chosen naturally with respect to the original assignments.
- Subjects
MATHEMATICAL functions; COMMUTATIVE algebra; HOMOTOPY theory; MORPHISMS (Mathematics); MATHEMATICAL mappings
- Publication
Journal of Homotopy & Related Structures, 2018, Vol 13, Issue 2, p273
- ISSN
2193-8407
- Publication type
Article
- DOI
10.1007/s40062-017-0182-2