Identity Categories as Potential Coalitions

Restriction categories as enriched categories

Article history: Received 27 November 2012 Received in revised form 4 September 2013 Accepted 20 December 2013 Communicated by B.P.F. Jacobs

Weak identity arrows in higher categories

There are a dozen definitions of weak higher categories, all of which loosen the notion of composition of arrows. A new approach is presented here, where instead the notion of identity arrow is weakened — these are tentatively called fair categories. The approach is simplicial in spirit, but the usual simplicial category ∆ is replaced by a certain ‘fat’ delta of ‘coloured ordinals’, where the d...

Dependencies As Categories

Directed Containers as Categories

Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a directed container morphism those of a monoid morphism in the reverse direction. With some reorganization, a directed container is the same as a small catego...

Finite Inverse Categories as Signatures

We define a simple dependent type theory and prove that its wellformed types correspond exactly to finite inverse categories.