Codescent objects and coherence
Codescent objects and coherence
复制标题
共下降物体和连贯性
DOI：
10.1016/s0022-4049(02)00136-6
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发表时间：
2002
影响因子：
0.8
通讯作者：
Stephen Lack
中科院分区：
文献类型：
--
作者：
Stephen Lack
我们描述了相干数据的2范畴共限概念，即相干数据的共限对象和松弛共限对象，并利用它们研究了2-单点T的2范畴严格T代数和严格T态射在伪T代数和伪T态射的2范畴中的包涵T- algs→Ps-T- Alg；类似地包含T-Algs→lax - t - alg，其中lax - t - alg有松弛代数和松弛态射，而不是伪代数。我们给出了这些内含物留下伴随的充分条件。我们给出了第一包含有左伴随且单位分量相等的充分条件，使得每个伪代数都等价于一个严格的伪代数。
We describe 2-categorical colimit notions called codescent objects of coherence data, and lax codescent objects of lax coherence data, and use them to study the inclusion, T-Algs→Ps-T- Alg, of the 2-category of strict T-algebras and strict T-morphisms of a 2-monad T into the 2-category of pseudo T-algebras and pseudo T-morphisms; and similarly the inclusion T-Algs→Lax-T-Algℓ, where Lax-T-Algℓhas lax algebras and lax morphisms rather than pseudo ones. We give sufficient conditions under which these inclusions have left adjoints. We give sufficient conditions under which the first inclusion has left adjoint for which the components of the unit are equivalences, so that every pseudo algebra is equivalent to a strict one.