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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         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.
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...
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...
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".
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...
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...
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...
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...
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...
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...
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 ...

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