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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
Our central observation is that model categories are the objects of a double category whose vertical and horizontal ar- rows are left and right Quillen functors, respectively, and
Note that the action of E on the members of G is what enables us to make some sense of the notion of fundamental n -category for these globular sets despite the fact that a priori
However, it cannot be completely lifted since in the last example we presented a locally finitely presentable category which, although it is a topos, has non- unique strict solutions
Remark 9 The category C( A ), equipped with the set of short exact sequences that have zero connectors on homology as pure short exact sequences, is an exact category with
The notion of a differential category provides a basic axiomatization for differential operators in monoidal categories, which not only generalizes the work of Ehrhard and Regnier
For a general semigroup T , the topos of presheaves on a category L ( T ) is not necessarily ap- propriate as its classifying topos mainly because of fact that general semigroups
Now since q preserves limits as well as colimits (by Proposition 2.4), it follows from Theorem 2.2 that the equifier subcategory inside the category of coalgebras is a
