Higher weak (co)limits, adjoint functor theorems, and higher Brown representability
نویسندگان
چکیده
We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $\infty$-categories -- in particular, these do not admit all small (co)limits general. also introduce Brown representability (homotopy) and a theorem localizations compactly generated presentable if $n \geq 2$ stable any 1$.
منابع مشابه
Steps toward the weak higher category of weak higher categories in the globular setting
We start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{Cambat}. As in cite{Cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{N}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. The last chapter of this article asserts that, up to precise...
متن کاملHigher categories, colimits, and the blob complex.
We summarize our axioms for higher categories, and describe the "blob complex." Fixing an n-category , the blob complex associates a chain complex B(*)(W;C) to any n-manifold W. The zeroth homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W = S(1)...
متن کاملsteps toward the weak higher category of weak higher categories in the globular setting
we start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{cambat}. as in cite{cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{n}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. the last chapter of this article asserts that, up to precise...
متن کاملContinuity is an Adjoint Functor
1. INTRODUCTION. The emergence of category theory, introduced by S. Eilen-berg and S. Mac Lane in the 1940s (cf. [2]), was among the most important mathematical developments of the twentieth century. The profound impact of the theory continues to this day, and categorical methods are currently used, for example, in algebra, geometry, topology, mathematical physics, logic, and theoretical comput...
متن کاملBrown Representability and Flat Covers
We exhibit a surprising connection between the following two concepts: Brown representability which arises in stable homotopy theory, and flat covers which arise in module theory. It is shown that Brown representability holds for a compactly generated triangulated category if and only if for every additive functor from the category of compact objects into the category of abelian groups a flat c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Documenta Mathematica
سال: 2022
ISSN: ['1431-0635', '1431-0643']
DOI: https://doi.org/10.4171/dm/900