3 citations · 4 across the 7 of their papers we have counts for
4 papers · 1 filter
Simplicial sets with a notion of smallness
M. Gavrilovich
We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reform…
A naive diagram-chasing approach to formalisation of tame topology
Misha Gavrilovich, Konstantin Pimenov
We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonali…
Topological and metric spaces are full subcategories of the category of simplicial objects of the category of filters
Misha Gavrilovich
We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplic…
The unreasonable power of the lifting property in elementary mathematics
Misha Gavrilovich
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a numb…