scholarly journals Hopf Cyclic Cohomology in Non-symmetric Monoidal Categories

2015 ◽  
Vol 3 (6) ◽  
pp. 157-163
Author(s):  
Arash Pourkia
Keyword(s):  
Cyclic Cohomology ◽  
Monoidal Categories ◽  
Symmetric Monoidal Categories ◽  
Hopf Cyclic Cohomology

scholarly journals Monoidal Categories, 2-Traces, and Cyclic Cohomology

2019 ◽  
Vol 62 (02) ◽  
pp. 293-312 ◽  
Author(s):  
Mohammad Hassanzadeh ◽  
Masoud Khalkhali ◽  
Ilya Shapiro
Keyword(s):  
Associative Algebra ◽  
Monoidal Category ◽  
Cyclic Homology ◽  
Cyclic Cohomology ◽  
Monoidal Categories ◽  
Central Pair ◽  
Cyclic Type ◽  
Unital Associative Algebra

AbstractIn this paper we show that to a unital associative algebra object (resp. co-unital co-associative co-algebra object) of any abelian monoidal category ( $\mathscr{C},\otimes$ ) endowed with a symmetric 2-trace, i.e., an $F\in \text{Fun}(\mathscr{C},\text{Vec})$ satisfying some natural trace-like conditions, one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra “with coefficients in $F$ ”. Furthermore, we observe that if $\mathscr{M}$ is a $\mathscr{C}$ -bimodule category and $(F,M)$ is a stable central pair, i.e., $F\in \text{Fun}(\mathscr{M},\text{Vec})$ and $M\in \mathscr{M}$ satisfy certain conditions, then $\mathscr{C}$ acquires a symmetric 2-trace. The dual notions of symmetric 2-contratraces and stable central contrapairs are derived as well. As an application we can recover all Hopf cyclic type (co)homology theories.

scholarly journals Hopf cyclic cohomology and Hodge theory for proper actions

2013 ◽  
Vol 7 (3) ◽  
pp. 885-905 ◽  
Author(s):  
Xiang Tang ◽  
Yi-Jun Yao ◽  
Weiping Zhang
Keyword(s):  
Hodge Theory ◽  
Cyclic Cohomology ◽  
Proper Actions ◽  
Hopf Cyclic Cohomology

scholarly journals Galois Theory in Symmetric Monoidal Categories

1999 ◽  
Vol 220 (1) ◽  
pp. 174-187 ◽  
Author(s):  
George Janelidze ◽  
Ross Street
Keyword(s):  
Galois Theory ◽  
Monoidal Categories ◽  
Symmetric Monoidal Categories
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