Related papers: Cartesian closed categories are distributive
The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our…
Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
We introduce and develop the notion of *displayed categories*. A displayed category over a category C is equivalent to "a category D and functor F : D --> C", but instead of having a single collection of "objects of D" with a map to the…
When formalizing mathematics in (generalized predicative) constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we…
There is a well-known correspondence between coherent theories (and their interpretations) and coherent categories (resp. functors), hence the (2,1)-category $\mathbf{Coh_{\sim}}$ (of small coherent categories, coherent functors and all…
The present paper gives a generalization of cartesian closed categories, called cartesian closed categories with dependence, whose strict version induces categories with families that support 1-, Sigma- and Pi-types in the strict sense.…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusions (via discrete fibrations and opfibrations) of the left and of the right actions of X in Cat in categories over X. Namely, a "weak…
We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also…
We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of…
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of…
Category theory provides a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of the…
An argument of A.Borel shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an…
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
A skeleton of the category with finite coproducts D freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products C freely generated by a countable set of objects. As a consequence, we…
We describe all left continuous triangular norms for which the category [0,1]-Cat of real-enriched categories and functors is cartesian closed. We furthermore show that the cartesian closedness of [0,1]-Cat is equivalent to the cartesian…
In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the existence of certain types of functorial factorizations. On our…
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…