Cylinders and paths in simplicial categories
Seunghun Lee
TL;DR
This paper establishes fundamental properties of cylinder and path objects in closed simplicial model categories, ensuring their uniqueness, functoriality, and naturality, which are crucial for homotopical constructions.
Contribution
It proves the uniqueness, functoriality, and naturality of cylinder and path objects in closed simplicial model categories, clarifying their structural role.
Findings
Cylinder and path objects are unique up to isomorphism.
They are functorial with respect to morphisms.
They exhibit naturality properties in the model category context.
Abstract
We prove the uniqueness, the functoriality and the naturality of cylinder objects and path objects in closed simplicial model categories.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis