Torsion free types
Torsion in K2 of fields and 0-cycles on rational surfaces.
Torsion in one-term distributive homology
The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely....
Torsion Theories in Non-Additive Categories.
Torsors and special extensions
Totality of colimit closures
Adámek, Herrlich, and Reiterman showed that a cocomplete category is cocomplete if there exists a small (full) subcategory such that every -object is a colimit of -objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions...
Totality of product completions
Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category by asking the Yoneda embedding to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion of . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product...
Toute théorie est algébrique et topologique
Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body
Towards a logic of semiotic systems
The rationalistic denotational approach to semantics is not adequate for capturing the structural dimension of meaning, which is immanent in semiotic systems. The demand for a structural approach to semantics is intensified by a turn in Artificial Intelligence, introduced by Connectionism and Information Retrieval. This paper presents such a structural approach to semantics founded on the phenomenological and autopoietic paradigms and proposes a formalization with the help of category theory.
Towards a sketch based model of self-interpreters
Towards an -category of cobordisms.
Tower extension of topological constructs
Let be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct , called the tower extension of (indexed by ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot...
Traced premonoidal categories
Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in cartesian categories.
Traced Premonoidal Categories
Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in Cartesian categories.
Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées
Trames et sémantiques catégoriques des systèmes de trames
Transfer of derived equivalences from subalgebras to endomorphism algebras II
We investigate derived equivalences between subalgebras of some -Auslander-Yoneda algebras from a class of -angles in weakly -angulated categories. The derived equivalences are obtained by transferring subalgebras induced by -angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to -angle cases. Finally, we give an explicit example to illustrate our result.
Transformation de Fourier géométrique et microlocalisation
Transformations of sheaf connections.