Projects per year
We consider an extant infinitary variant of Lawvere’s deﬁnition of extensivity of a category V. In the presence of cartesian closedness and ﬁnite limits in V, we give two characterisations of the condition in terms of a biequivalence between the bicategory of matrices over V and the bicategory of spans over discrete objects in V. Using the condition, we prove that V-Cat and the category Catd(V) of internal categories in V with a discrete object of objects are equivalent. Our leading example has V = Cat, making V-Cat the category of all small 2-categories and Catd(V) the category of small double categories with discrete category of objects. We further show that if V is extensive, then so are V-Cat and Cat(V), allowing the process to iterate.
|Number of pages||16|
|Journal||Tbilisi Mathematical Journal|
|Publication status||Published - 1 Jun 2017|
- internal category
ASJC Scopus subject areas
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- 1 Finished
Higher Category Theoretic Structure of Programming Semantics
11/11/16 → 11/11/18
Project: Research council