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If we take as D the empty doctrine, we have a duality between the 2-category of small Cauchy complete categories, functors and natural transformations, and the 2-category of
If the pointed Set -functor T satisfies (BC) and V is a complete and cocomplete locally cartesian closed category, then Alg( T, V ) is a
However, from the result of Volger already mentioned in 3.3(b), there exist reflective subcategories of locally finitely presentable categories which are closed under directed
In Section 2, we show that while copower objects do not produce as simple a definition of a topos, for a pretopos (a coherent category in which all equivalence relations occur as
As a small dense subcategory representing finitely presentable objects we can choose categories on finitely many objects subject to a finite set of commutativity
It is convenient to work in a cartesian closed category (e.g. sequential spaces ); this yields nice spaces of measurable functions and nice spaces of measures.. Then σ -additivity
One can find different de- scriptions (not as crossed modules) of internal categories and groupoids in groups, Mal’tsev varieties of universal algebras, congruence modular vari-
When we look at continuous categories with a small dense subcategory (in connection to the generalized powerdomain constructions), we regard as the appropriate version of the
