Finite sets and symmetric simplicial sets
By Marco De Grandis. Theory and Applications of Categories, 2001
48 citations recorded by the source corpus.
The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal symmetric monoid, or by generators and relations. The latter provides a definition of symmetric simplicial sets by faces, degeneracies and transpositions, under suitable relations.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dee164ed991c25c6ccabf7db07f482166c7a9575
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Cubical sets and their site (2003, unknown): “The categoryõf finite ordinals (and monotone mappings) is the basis of the presheaf category Smp ∼ of augmented simplicial sets, i.e. functors X : ˜”
- Tensor categorical foundations of algebraic geometry (2014, background): “This is the universal tensor category equipped with a commutative monoid object ([Gra01]) and hence its free cocompletion F̂inSet is the universal cocomplete”