Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Motivic Tambara functors
View through CrossRef
AbstractLet k be a field and denote by $$\mathcal {SH}(k)$$
SH
(
k
)
the motivic stable homotopy category. Recall its full subcategory $$\mathcal {SH}(k)^{{\text {eff}}\heartsuit }$$
SH
(
k
)
eff
♡
(Bachmann in J Topol 10(4):1124–1144. arXiv:1610.01346, 2017). Write $$\mathrm {NAlg}(\mathcal {SH}(k))$$
NAlg
(
SH
(
k
)
)
for the category of $${\mathrm {S}\mathrm {m}}$$
S
m
-normed spectra (Bachmann-Hoyois in arXiv:1711.03061, 2017); recall that there is a forgetful functor $$U: \mathrm {NAlg}(\mathcal {SH}(k)) \rightarrow \mathcal {SH}(k)$$
U
:
NAlg
(
SH
(
k
)
)
→
SH
(
k
)
. Let $$\mathrm {NAlg}(\mathcal {SH}(k)^{{\text {eff}}\heartsuit }) \subset \mathrm {NAlg}(\mathcal {SH}(k))$$
NAlg
(
SH
(
k
)
eff
♡
)
⊂
NAlg
(
SH
(
k
)
)
denote the full subcategory on normed spectra E such that $$UE \in \mathcal {SH}(k)^{{\text {eff}}\heartsuit }$$
U
E
∈
SH
(
k
)
eff
♡
. In this article we provide an explicit description of $$\mathrm {NAlg}(\mathcal {SH}(k)^{{\text {eff}}\heartsuit })$$
NAlg
(
SH
(
k
)
eff
♡
)
as the category of effective homotopy modules with étale norms, at least if $$char(k) = 0$$
c
h
a
r
(
k
)
=
0
. A weaker statement is available if k is perfect of characteristic $$> 2$$
>
2
.
Title: Motivic Tambara functors
Description:
AbstractLet k be a field and denote by $$\mathcal {SH}(k)$$
SH
(
k
)
the motivic stable homotopy category.
Recall its full subcategory $$\mathcal {SH}(k)^{{\text {eff}}\heartsuit }$$
SH
(
k
)
eff
♡
(Bachmann in J Topol 10(4):1124–1144.
arXiv:1610.
01346, 2017).
Write $$\mathrm {NAlg}(\mathcal {SH}(k))$$
NAlg
(
SH
(
k
)
)
for the category of $${\mathrm {S}\mathrm {m}}$$
S
m
-normed spectra (Bachmann-Hoyois in arXiv:1711.
03061, 2017); recall that there is a forgetful functor $$U: \mathrm {NAlg}(\mathcal {SH}(k)) \rightarrow \mathcal {SH}(k)$$
U
:
NAlg
(
SH
(
k
)
)
→
SH
(
k
)
.
Let $$\mathrm {NAlg}(\mathcal {SH}(k)^{{\text {eff}}\heartsuit }) \subset \mathrm {NAlg}(\mathcal {SH}(k))$$
NAlg
(
SH
(
k
)
eff
♡
)
⊂
NAlg
(
SH
(
k
)
)
denote the full subcategory on normed spectra E such that $$UE \in \mathcal {SH}(k)^{{\text {eff}}\heartsuit }$$
U
E
∈
SH
(
k
)
eff
♡
.
In this article we provide an explicit description of $$\mathrm {NAlg}(\mathcal {SH}(k)^{{\text {eff}}\heartsuit })$$
NAlg
(
SH
(
k
)
eff
♡
)
as the category of effective homotopy modules with étale norms, at least if $$char(k) = 0$$
c
h
a
r
(
k
)
=
0
.
A weaker statement is available if k is perfect of characteristic $$> 2$$
>
2
.
Related Results
Around evaluations of biset functors
Around evaluations of biset functors
Our purpose here, is to study double Burnside algebras via evaluations of biset functors. In order to avoid the difficult problem of vanishing of simple functors, we look at finite...
Stratifications and Mackey Functors II: Globally Defined Mackey Functors
Stratifications and Mackey Functors II: Globally Defined Mackey Functors
AbstractWe describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero the...
A Categorical Framework for Program Semantics and Semantic Abstraction
A Categorical Framework for Program Semantics and Semantic Abstraction
Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation...
Homotopy Theory of Enriched Mackey Functors
Homotopy Theory of Enriched Mackey Functors
This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagra...
FUNCTORS AND SPACES IN IDEMPOTENT MATHEMATICS
FUNCTORS AND SPACES IN IDEMPOTENT MATHEMATICS
Idempotent mathematics is a branch of mathematics in which idempotent operations (for example, max) on the set of reals play a central role. In recent decades, we have seen intensi...
Generalised powerlocales via relation lifting
Generalised powerlocales via relation lifting
This paper introduces an endofunctor VT on the category of frames that is parametrised by an endofunctor T on the category Set that satisfies certain constraints. This generalises ...
Transport of finiteness structures and applications
Transport of finiteness structures and applications
We describe a general construction of finiteness spaces which subsumes the interpretations of all positive connectors of linear logic. We then show how to apply this construction t...
Transfinite Fixed-Point Resolution of Open Problems in Alpay Algebra
Transfinite Fixed-Point Resolution of Open Problems in Alpay Algebra
We introduce a transfinite fixed-point operator, denoted $\phi^\infty$, within the framework of Alpay Algebra---a categorical foundation for mathematical structures. This operator,...