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2-范畴中拉回的若干性质
2-范畴 相对正合2-范畴 拉回 核
2013/11/28
从相对正合2-范畴S出发,给出了2-范畴中拉回的若干性质.首先,证明了拉回在等价意义下是存在且唯一的; 其次,设(A1×BA2,f’1,f’2,ξ)为f1与f2的拉回,证明了Ker(f1)与Ker(f’2)等价,Ker(f2)与Ker(f’1)等价; 最后,证明了大方框拉回与小方框拉回之间联系的相关结论.
We characterize the category of monads on $Set$ and the category of Lawvere theories that are equivalent to the category of regular equational theories.
A colimit decomposition for homotopy algebras in Cat
A colimit decomposition homotopy algebras Cat Category Theory
2012/6/25
Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky o...
Rigidification of algebras over essentially algebraic theories
homotopy limit theory homotopy model rigidification
2012/6/18
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result can be extended from...
We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds effective quotients...
We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg--Moore category C^T that classifies bimorphisms. The category of action...
Skew monoidales, skew warpings and quantum categories
bialgebroid fusion operator quantum category monoidal bicategory monoidale skew-monoidal category
2012/5/9
Kornel Szlach\'anyi recently used the term skew-monoidal category for a particular laxified version of monoidal category. He showed that bialgebroids $H$ with base ring $R$ could be characterized in t...
We make some remarks on the foundations of the homotopy theory of enriched precategories, as exposed in Carlos Simpson's book "Homotopy theory of higher categories".
Gluing derived equivalences together
Grothendieck constructions oplax functors derived equivalences
2012/4/17
The Grothendieck construction of a diagram X of categories can be seen as a process to construct a single category Gr(X) by gluing categories in the diagram together. Here we formulate diagrams of cat...
Not every object in the derived category of a ring is Bousfield equivalent to a module
Not every object derived category ring Bousfield equivalent module
2012/3/1
We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
Traces in symmetric monoidal categories
Traces symmetric monoidal categories Category Theory
2011/9/29
Abstract: The purpose of this expository note is to describe duality and trace in a symmetric monoidal category, along with important properties (including naturality and functoriality), and to give a...
Causal categories: relativistically interacting processes
Causal categories General Relativity and Quantum Cosmology Category Theory
2011/10/10
Abstract: A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This stru...
Pseudogroups and their etale groupoids
Inverse semigroups etale topological groupoids locales topos theory
2011/9/22
Abstract: A pseudogroup is a complete infinitely distributive inverse monoid. Such inverse monoids bear the same relationship to classical pseudogroups of transformations as frames do to topological s...
On the derived category of a graded commutative noetherian ring
Localizing subcategories graded ring weighted projective scheme
2011/9/20
Abstract: For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijec...
Injective objects and retracts of Fraisse limits
Fraisse limit retract injective object amalgamation pushout
2011/9/19
Abstract: We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a ...