We show that every λm-injectivity class (i.e., the class of all the objects injective with respect to some class of λ-presentable morphisms) is a weakly reflective subcategory determined by a functorial weak factorization system cofibrantly generated by a class of λ-presentable morphisms. This was known for small-injectivity classes, and referred to as the “small object argument”. An analogous ...

This work is a contribution to a recent field, Directed Algebraic Topology. Categories which appear as fundamental categories of ‘directed structures’, e.g. ordered topological spaces, have to be studied up to appropriate notions of directed homotopy equivalence, which are more general than ordinary equivalence of categories. Here we introduce past and future equivalences of categories—sort of ...

We show that the category of internal groupoids in an exact Mal'tsev is reflective, and fact a Birkhoff subcategory simplicial objects. then characterize central extensions corresponding Galois structure, regular epimorphisms admit relative monotone-light factorization system sense Chikhladze. also draw some comparison with Kan complexes. By comparing reflections objects reflexive graphs into g...

This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and trace monoid actions are constructed. These functors carry independence preserving morphisms in th...

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

This paper deals with several aspects of epimorphisms in the category MFrm of metric frames and contractive homomorphisms. In particular, it is shown that (i) the epicomplete metric frames are uniquely determined by the power-set lattices of sets, (ii) episurjective is the same as Boolean, (iii) a metric frame has an epicompletion iff it is spatial, and (iv) the subcategory of epicomplete L in ...

We use a K-theory recipe of Thomason to obtain classi cations of triangulated subcategories via re ning some standard thick subcategory theorems. We apply this recipe to the full subcategories of nite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classi cation of the triangulated subcategories of perfect...

We introduce an endofunctor H on the category baℓ of bounded archimedean ℓ-algebras and show that there is a dual adjunction between Alg(H) algebras for Coalg(V) coalgebras Vietoris V compact Hausdorff spaces. prove Gelfand duality lifts to equivalence full reflective subcategory Algu(H) Alg(H). provide alternate view by introducing Hu consisting uniformly complete objects showing Alg(Hu) isomo...