Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn reflective subcategories of locally presentable categories
93
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Are all subcategories of locally finitely presentable categories that are closed under limits and $lambda$-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case $lambda=aleph_0$ the answer is affirmative also for all iso-full subcategories, emph{i.thinspace e.}, those containing with every pair of objects all isomorphisms between them. We discuss a possible generalization of this from $aleph_0$ to an arbitrary $lambda$.
rate research
Read More
We prove that every locally Cartesian closed $infty$-category with subobject classifier has a strict initial object and disjoint and universal binary coproducts.
We define filter quotients of $(infty,1)$-categories and prove that filter quotients preserve the structure of an elementary $(infty,1)$-topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of $(infty,1)$-categories and prove a characterization theorem for equivalences in a filter product. Then we use filter products to construct a large class of elementary $(infty,1)$-toposes that are not Grothendieck $(infty,1)$-toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an $(infty,1)$-category, but would prefer to avoid the technicalities regarding filters.
In this paper, we have studied the axiomatics of {it Ann-categories} and {it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have achieved is proving the independence of the axiomatics of Ann-category definition. And then we have proved that after adding an axiom into the definition of categorical rings, we obtain the new axiomatics which is equivalent to the one of Ann-categories.
The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functionals defined on category algebras. We clarify that category algebras can be considered as generalized matrix algebras and that states on categories as linear functionals defined on category algebras turn out to be generalized of probability measures on sets as discrete categories. Moreover, by establishing a generalization of famous GNS (Gelfand-Naimark-Segal) construction, we obtain representations of category algebras of $^{dagger}$-categories on certain generalized Hilbert spaces which we call semi-Hilbert modules over rigs.
We introduce partially lax limits of infinity-categories, which interpolate between ordinary limits and lax limits. Most naturally occurring examples of lax limits are only partially lax; we give examples arising from enriched categories and operads. Our main result is a formula for partially lax limits and colimits in terms of the Grothendieck construction. This generalizes a formula of Lurie for ordinary limits and of Gepner-Haugseng-Nikolaus for fully lax limits.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
