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More precisely, the homotopy double groupoid is a double groupoid with connection which, under the equivalence of categories between small 2-categories and double categories
Namely, new factorization systems are constructed on the categories of Abelian groups (more generally, on any Abelian category), groups with unary operators, locally com- pact
The fibrant functors are precisely the pointwise fibrant functors which preserve weak equivalences, thus any enriched functor is weakly equivalent in the homotopy functor model
ized pullback and finite coproduct preserving functors between categories of permutation representations of finite groups.. Initially surprising to a category theorist, this result
Note that a finitely accessible abelian category is necessarily locally finitely pre- sentable, and also that a locally finitely presentable pointed category is abelian if and only
We show that every KZ- doctrine is a pseudomonad (pseudomonoid in the Gray monoid determined by an object of the Gray -category), and that the 2-categories of algebras dened
In [CKW] the theory was illustrated in detail with a section devoted to rel seen as a colax functor from the 2-category REG of regular categories, arbitrary functors, and
If Φ is a small class of weights we can define, as we did for J -Colim, a2-category Φ- Colim of small categories with chosen Φ-colimits, functors preserving these strictly, and
