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Results tagged with internal-categories
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user 152679
5
votes
Internal $2$-categories
Bicategories internal to 2-categories with pullbacks are defined in §3 of Douglas–Henriques's Internal bicategories. They have two motivating examples described in §1: a bicategory $\mathrm{Bord}_0^2$ …
- 10.7k
8
votes
J.W. Gray's monumental work notes on the formal theory of internal (2-)categories
I asked Peter Johnstone about this citation, and he told me that he included the reference, despite not having a copy of the manuscript, since John Gray had been promising a book on the subject for ma …
- 10.7k
10
votes
Accepted
Standard reference for double category theory
The short answer is that, no, there does not (yet) exist a good introduction/reference for double category theory. Part of the reason for this is that double category theory only started to enjoy a su …
- 10.7k
1
vote
0
answers
131
views
Universal property of the V-Mat construction
Internal categories and enriched categories can both be realised as monads in certain bicategories. If $\mathcal E$ is a category with pullbacks, then a monad in $\mathbf{Span}(\mathcal E)$ is a categ …
- 10.7k