Let C be a category with strong monomorphic strong coimages, that is, every morphism ƒ of C factors as ƒ = u ° g so that g is a strong epimorphism and u is a strong monomorphism and this factorization is universal. We define the notion of strong Mittag-Leffler property in pro-C. We show that if ƒ : X → Y is a level morphism in pro-C such that ( ) p Y ! " is a strong epimorphism for all β > α, t...

In this paper, we propose a new,loose semantics for place/transition nets based on transition systems and generalizing the reachability graph semantics. The loose semantics of a place/transition net reflects all its possible refinements and is given as a category of transition systems with alternative sequences of events over the net. The main result states that each plain morphism between two ...

We study the structure of the flow monoid of a regular semigroup. This arises from the approach of Nambooripad of considering a regular semigroup as a groupoid – a category in which every morphism is invertible. A flow is then a section to the source map in this groupoid, and the monoid structure of the set of all flows is determined in terms of the Green relations on the original semigroup.

In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category K is introduced, as a pair (comonad, monad) over K. The link with existing notions in terms of morphism classes is given via the respective Eilenberg–Moore categories. Dedica...

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents. Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the morphism space D(s,Σs) is k for i = 0 and i = 2 and vanishes otherwise. Assume that s classically generates D, that is, each object of D can be built from s using (de)suspensions, direct sums, direct summands, ...

where ◦o1,o2,o3 : 〈o2,o3〉×〈o1,o2〉 → 〈o1,o3〉 that satisfies usual conditions (associativity and the existence of the identities). This approach is closer to the way in which categories are presented in homological algebra (e.g. [1], pp.58-59). We do not assume that 〈o1,o2〉’s are mutually disjoint. If f is simultaneously a morphism from o1 to o2 and o1 to o2 (o1 6= o1) than different compositions...

It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group coherently extended along any outgoing homomorphism. One is thus motivated to define a notion (categorical) automorphism in an arbitrary category, morphism, theory such forms part covariant isotropy. In this paper, we prove categorical category $$\textsf{Group...

We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-ReshetikhinTuraev TQFTs associated to SU(2) and SO(3) induce linear representations of this group. We show that the denominators of matrices which describe these representations over a cyclotomic field can be restricted in many cases. In this way, we give a proof of the...

Let Q be a finite acyclic valued quiver. We define bialgebra structure and an integration map on the Hall algebra associated to morphism category of projective representations Q. As application, we recover surjective homomorphism defined in [12], which realizes principal coefficient quantum cluster $$\mathcal {A}\,_q(Q)$$ as sub-quotient morphisms. Moreover, also Caldero–Chapoton formula, well ...