123 citations · 583 across the 42 of their papers we have counts for
23 papers · 1 filter
The eventual image
Tom Leinster
In a category with enough limits and colimits, one can form the universal automorphism on an endomorphism in two dual senses. Sometimes these dual constructions coincide, as in the…
Isbell conjugacy and the reflexive completion
Tom Avery, Tom Leinster
The reflexive completion of a category consists of the Set-valued functors on it that are canonically isomorphic to their double conjugate. After reviewing both this construction a…
Basic Category Theory
Tom Leinster
This short introductory category theory textbook is for readers with relatively little mathematical background (e.g. the first half of an undergraduate mathematics degree). At its…
Notes on commutation of limits and colimits
Marie Bjerrum, Peter Johnstone, Tom Leinster +1
We show that there are infinitely many distinct closed classes of colimits (in the sense of the Galois connection induced by commutation of limits and colimits in Set) which are in…
Weak -categories via terminal coalgebras
Eugenia Cheng, Tom Leinster
Higher categorical structures are often defined by induction on dimension, which a priori produces only finite-dimensional structures. In this paper we show how to extend such defi…
Codensity and the ultrafilter monad
Tom Leinster
Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity mon…