Directory UMM :Journals:Journal_of_mathematics:OTHER:
Teks penuh
Dokumen terkait
In [2], classes of objects injective with respect to a set M of morphisms of a locally presentable category K were characterized: they are precisely the classes closed under products,
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
We begin with the introduction of the category Rel B of relational variable sets and morphisms, and its equivalence to Cat f /B.. We conclude, in § 5, with an application to
This classifying topos contains as a cartesian closed reflective subcategory the category of all groupoids (= small categories in which every morphism is invertible) just as
The main observation is that each one of the above classes of categories can be obtained as the class of finitely complete categories (or pointed categories) with M -closed relations
We saw in the prologue that the comonad Path on Cat has as its coalgebras free categories on graphs (the category of coalgebras is equivalent to the category of graphs), and that
Given a double category with companions, one can construct a pointed equipment by using the same objects, defining the scalar arrows to be the vertical arrows of the double
This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in
