Are Banach spaces monadic?

Monadic forgetful functors and (non-)presentability for $C^*$- and $W^*$-algebras

We prove that the forgetful functors from the categories of $C^*$- and $W^*$-algebras to Banach $*$-algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosický, and that the categories of unital (commutative) $C^*$-algebras are not locally-isometry $\aleph_0$-generated either as plain or as metric-enriched categories, answering a question of I. Di Liberti and Rosický. We also prove a number of negative presentability results for the category of von Neumann algebras: not only is that category not locally presentable, but in fact its only presentable objects are…

算子代数范畴中遗忘函子的局部可表现性与单子性

Local presentability and monadicity of forgetful functors for operator algebraic categories

本研究将完备算子空间范畴的局部可数可表现性结论推广到非完备情形，证明算子系统等范畴的该性质，厘清多类算子代数相关范畴间遗忘函子的伴随性与单子性，并借助Kadison对偶定理研究函数论子范畴的相关性质。

关于单子向量值积分

On Monadic Vector-Valued Integration

本文在hk-空间范畴上构造交换概率单子，发展配对线性hk-空间理论，并通过自由-遗忘伴随自然导出单子向量值积分理论。

严格单子拓扑 II：闭包空间的下降

Strict monadic topology II: descent for closure spaces

本文开创闭包空间的下降理论，主要贡献是刻画了下降态射，并证明了有限闭包空间范畴中下降态射均为有效下降态射，且满射闭映射与满射开映射均为有效下降态射。

Monadic Decompositions and Classical Lie Theory

We show that the functor from bialgebras to vector spaces sending a bialgebra to its subspace of primitives has monadic length at most 2.

Restricted Lie algebras via monadic decomposition

We give a description of the category of restricted Lie algebras over a field $\Bbbk $ of prime characteristic by means of monadic decomposition of the functor that computes the $\Bbbk $-vector space of primitive elements of a $\Bbbk $-bialgebra.